%( expression1, expression2, ... ) — Expression evaluation function

Used to group sub-calculations in situations where a comma would be interpreted as an argument separator. For instance, in

 

%if( x>=0, %(y=sqrt(x),x), y=%na)

 

if X is non-negative, this returns X while setting Y to the square root of X. If X is negative, this returns a missing value while also setting Y to the missing value. %(expr1,expr2,…,exprn) returns the value of the final expression in the group.

 

 

abs(x),%abs(A) — Absolute value of a scalar or matrix

For a scalar argument, ABS returns the absolute value of the scalar. For matrix argument A, %ABS returns a matrix with the absolute values of the corresponding elements of A.

 

 

%acos(x) — Arc (inverse) cosine

Returns the inverse cosine of its argument.
 

 

%allocend() — Default series workspace length

This returns the length of the default workspace length, which is usually set using the ALLOCATE or first DATA instruction.

 

 

%annuity(p,r,n) — Present value of an annuity

Returns the present value of an annuity with payment p, interest rate r, and term n.
 

 

%arg(z) — Argument of a complex number

Returns the argument of a complex number. This is \({\tan ^{ - 1}}\left( {a/b} \right)\) for \(z = a + ib\)
 

 

%asin(x) — Arc (inverse) sine

Returns the inverse sine of its argument

 

 

%atan(x) — Arc (inverse) tangent

Returns the inverse tangent of its argument
 

 

%avg(A) — Average of matrix elements

Returns the average of the elements of A. If A is symmetric, off-diagonal elements are counted only once.

 

 

%besselj(n,x) — Bessel function

Returns the Bessel function of the first kind, for x given order n.

 

 

%bestrep(A,w) — “Best” representation

Returns a string giving a “picture” code (for use in DISPLAY, PRINT and other output instructions) which “best” represents the values in the array A using w positions. In general, this will use all w positions. %MINIMALREP is similar but cuts the number of decimal places if they would be zeros for all numbers.

 

 

%betainc(x,a,b) — Incomplete beta function

Returns the incomplete beta function of x given parameters a and b.

 

 

%bicdf(X,Y,rho) — Cumulative density function of bivariate standard Normal

Returns \(P(x<X,y<Y)\) for a bivariate standard Normal with correlation coefficient rho.
 

 

%bin(x,V) — Determine appropriate “bin” for a value

This returns an integer indicating which “bin” the value x would fall in given a vector V of boundary values defining the bins. For example,

 

%bin(2.5,||1.0,2.0,3.0,4.0||)

 

returns integer value 2, as the value 2.5 is in the range (2.0 to 3.0) for the second bin.

 

 

%binomial(n,k) — Binomial coefficient

Returns the binomial coefficient \(n(n - 1) \ldots (n - k + 1)/k!\) or its generalization to non-integers \(\frac{{\Gamma (n + 1)}}{{\Gamma (k + 1)\Gamma (n - k + 1)}}\).

 

 

%binomialcdf(k,n,p) — Cumulative Binomial Distribution

Returns the cumulative distribution of a binomial (number of successes \(\le k\) given \(n\) trials with probability \(p\)).

 

 

%binomialk(k,n,p) — Binomial Distribution Function

Returns the probability function for a binomial (number of successes equal to \(k\) given \(n\) trials with probability \(p\).

 

 

%block(m,n) — Get Number of Blocks

Gives number of blocks (starting with one) when partitioning m integers into blocks of size n. For example, %block(10,5)=2, %block(11,5)=3.

 

 

%blockdiag(VR) — Create a block diagonal matrix

Returns a matrix formed by placing the elements of VR (a VECTOR of RECTANGULAR arrays) in blocks down the diagonal, with all other elements of the created matrix set to zero. Note that the matrices in VR do not have to be square. The ~\ operator (diagonal concatenation) is usually easier to use.
 

 

%blockglue(G) — Matrix concatenation

The argument is an array of RECTANGULARS. %blockglue() concatenates these in both dimensions to form a single large matrix. The ~ and ~~ operators (horizontal and vertical concatenation) are usually easier to use.

 

 

%blocksplit(A,IX) — Matrix partitioning

Returns a RECTANGULAR of RECTANGULARs formed by splitting the input array into blocks with dimensions given by the elements of the index array IX.

 

 

%boxcox(x,y) — Box‑Cox transformation

Returns the Box-Cox transformation of x and y, which is given by the formula: \(({x^y} - 1)/y\), or log x for y=0.
 

 

%bqfactor(S,L) — Blanchard-Quah factorization

Returns the Blanchard-Quah factorization of S (covariance matrix of residuals) with L as the matrix of sums of lag coefficients. The factorization is computed as:

 

\(L{\left( {{L^{ - 1}}S{{L'}^{ - 1}}} \right)^{1/2}}\)

 

where the matrix square root is the Cholesky factorization. Note that after doing an ESTIMATE, S is available as the reserved variable %SIGMA, and L is available as %VARLAGSUMS. The function %MODELLAGSUMS can compute it for a model that has been modified.

 

 

%cabs(z) — Complex absolute value

Returns the absolute value of a complex number z. The result is real.

 

 

%cal(year,period) — Entry number of specified date

Returns the entry number corresponding to the specified period of the year, given the current CALENDAR setting. It is equivalent to the expression year:period. For frequencies such as daily and weekly that are not specified in periods per year, %cal(year,period) returns the entry for that “period” (day or week) of the year.
 

 

%calendar() — Save current CALENDAR setting

Returns the current CALENDAR setting, which can be saved into a variable. That variable can be used with the RECALL option on CALENDAR to reset the CALENDAR.
 

 

%cdf(x) — Cumulative density function of standard Normal

Returns \(\Phi (x)\), where \(\Phi \) is the CDF of the standard Normal.

 

 

%cexp(z) — Complex exp function

Returns complex \({e^z}\).

 

 

%checkname(name) — Check for name already defined

Returns 1 if the name (as a STRING) is already in the symbol table, and 0 if it isn't. Added with version 9.1.

 

 

%chisqr(x,r) — Chi-squared tail probability

Returns the tail probability of a \({\chi ^2}\) with r degrees of freedom, that is, the probability that a \({\chi ^2}\) random variable with r degrees of freedom exceeds x.
 

 

%chisqrdensity(x,r) — Chi-squared density

Returns the density at x of a \({\chi ^2}\) with r degrees of freedom
 

 

%chisqrnc(x,r,nc) — Non-central chi-squared CDF

Returns the CDF at x of a \({\chi ^2}\) with r degrees of freedom for a non-central chi-square, with non-centrality nc. Note that this is the CDF, not the tail probability.

 

 

%chisqrncdensity(x,r,nc) — Non-central chi-squared density

Returns the density at x of a non-central \({\chi ^2}\) with r degrees of freedom and noncentrality nc.

 

 

%choice(label) — Map Label to Option Choice

Allows you to specify an argument for a “choice” option on a built-in instruction by supplying the appropriate text label as the argument on %CHOICE. For example, you can select the BFGS estimation method on any applicable instruction by using METHOD=%CHOICE("BFGS"). Useful in PROCEDUREs.

 

 

%chol(S) — Cholesky decomposition

Returns the Cholesky decomposition of a SYMMETRIC matrix. For a matrix S, this returns a lower-triangular RECTANGULAR array F, such that \({\bf{FF'}} = {\bf{S}}\). S must be positive semi-definite. See also the %PSDFACTOR function. This is a synonym for %DECOMP, and was added with 10.0, as a clearer name for the calculation.

 

 

%clock(m,n) — Modified modular division

Does a modified form of modular division, returning [(m–1) modulo n] + 1. Maps to 1,...,n.

 

 

%clog(z) — Complex natural log

Returns complex \({\log _e}z\).

 

 

%closestdate(y,m,d,dow)  — Observance date (closest day of week)

Returns the number of the day within a month that is the closest occurrence of the specified day of the week (dow) to the date specified by y,m,d. For example, Martin Luther King Day is observed in the U.S. on the Monday closest to January 20th. Days of the week are handled as Monday=1 through Sunday=7, so:

 

compute day = %closestdate(2007,1,20,1)

 

returns 22, indicating the closest Monday occurs on 2007:1:22.

 

 

%closestweekday(y,m,d) — Observance date (closest Monday–Friday)

Returns the day number within the month of the weekday closest to the date specified by y,m,d. For example:

 

?%closestweekday(2004,7,4)

 

displays 5, because the closest weekday to that 4 July 2004 was July 5 (a Monday).

 

 

%cm(x) — Convert centimeters to inches

Returns the number of inches in x centimeters. Absolute sizes for graphs are provided in inches, so, for instance, a height=%cm(12.0) option will allow you to set the height to be 12 cm.

 

 

%cmplx(real,imag) — Complex number from real and imaginary parts

Converts two real numbers into a complex number. The first argument is the real part and the second is the imaginary part.
 

 

%cols(A) — Number of columns of a matrix

Returns the number of columns in a matrix. Returns the value 1 for arrays of type VECTOR (use %rows(A) or %size(A) to get the dimension of a VECTOR)

 

 

%compress(A,v) — Compress empty rows out of an array

Returns an array with the same number of columns as A, but with all rows removed for which the corresponding element of the vector v is zero. A and v must have the same number of rows.
 

 

%concat(first,last) — Concatenate two labels

Concatenates two label variables. This can also be done as first+last.

 

 

%conjg(z) — Complex conjugate

Returns the complex conjugate of z.

 

 

%const(x) — Fill matrix with a constant value

In an expression A = %const(x), fills all elements of the array A with the value x. See also %FILL,%ZEROS and %ONES.

 

 

%corr(A,B) — Correlation coefficient

Computes the correlation coefficient of the two arrays.

 

 

%corrtocv(C,V) — Convert correlation matrix to covariance matrix

Converts a correlation matrix (C) and a vector of variances (V) into a covariance matrix.
 

 

cos(x) — Cosine function

Returns the cosine of x, where x is in radians. If x is a matrix, transforms all elements.

 

 

%cosh(x) — Hyperbolic cosine

Returns the hyperbolic cosine of its argument \(\frac{{\exp (z) + \exp ( - z)}}{2}\)
 

 

%cot(x) — Cotangent function

Returns the cotangent of x.
 

 

%cov(A,B) — Covariance of two arrays

Returns the covariance of two arrays:  \(\frac{1}{{NM}}\sum\limits_{ij} {\left( {{{\bf{A}}_{ij}} - {\bf{\bar A}}} \right)\left( {{{\bf{B}}_{ij}} - {\bf{\bar B}}} \right)} \)
 

 

%cputime()— CPU Timer

Returns the CPU’s internal time in seconds. You can use this to determine the running time of a program, by comparing results of calls to %CPUTIME made at the beginning and at the end of the program.

 

 

%csc(x) — Cosecant function

Returns the cosecant of x.
 

 

%csqrt(z) — Complex Square root

Returns the complex square root of z.

 

 

%cvtocorr(V) — Converts a covariance matrix to correlations

Returns the correlation matrix C created from a covariance matrix V:  \({{\bf{C}}_{ij}} = {{\bf{V}}_{ij}}/\sqrt {{{\bf{V}}_{ii}}{{\bf{V}}_{jj}}} \)

 

 

%cxadj(Z) ­— Complex matrix adjoint (conjugate transpose)

Returns the (conjugate transpose) adjoint of a complex matrix.

 

 

%cxdiag(Z) — Complex diagonal matrix

Returns the diagonal complex matrix from a complex vector or \(1 \times N\) rectangular.

 

 

%cxeigdecomp(Z) — Complex eigen decompostion

Returns the eigen decomposition of a Hermitian complex matrix. The return is a VECT[CMATRIX] with two components—the first are the eigenvalues, the second the eigenvectors.

 

 

%cxinv(Z) — Complex matrix inverse

Returns the complex inverse of a complex array.

 

 

%cxsvd(Z) — Complex singular value decomposition

Returns the singular value decomposition of a complex (m×n) matrix Z. This is a VECTOR of three complex matrices, U, W and V, where \({\bf{Z}} = {\bf{U}}{\rm{ }}diag({\bf{W}}){\rm{ }}{{\bf{V}}^*}\) (where * denotes the conjugate transpose).

 

U and V are column-orthonormal matrices, that is \({{\bf{U}}^*}{\bf{U}} = I,{{\bf{V}}^*}{\bf{V}} = I\). All elements of W (the singular values of Z) are real (though they’re stored as complex) and are sorted from largest to smallest. W has dimensions min(m,n) by 1; U and V are dimensioned to conform with that.
 

 

%dateandtime( ) — Date and time stamp

Returns a string with the current date and time.

 

 

%datelabel(e) — Date label for a given date/entry number

Returns the date label of entry e in the current CALENDAR scheme, formatted as RATS does on, for instance, a PRINT instruction.
 

 

%day(e) — Day of month for entry e

Returns the day of the month (1–31) of entry e in the current CALENDAR scheme.  Defined only if that scheme has a “year month day” format.
 

 

%daycount(e) — Number of days covered by entry e

Returns the number of days in entry e in the current CALENDAR scheme.  For instance, if the CALENDAR is set for monthly data, %DAYCOUNT(2014:11) is 30. With quarterly data, %DAYCOUNT(2010:2) is 91.

 

 

%ddivide(A,v) — Divide columns of a matrix by vector elements

Returns the result of dividing the columns of A by corresponding elements in VECTOR v.

 

 

%decomp(S) — Cholesky decomposition

Returns the Cholesky decomposition of a SYMMETRIC matrix. For a matrix S, this returns a lower-triangular RECTANGULAR array F, such that \({\bf{FF'}} = {\bf{S}}\). S must be positive semi-definite. See also the %PSDFACTOR function.

 

 

%defined(name) — Status of procedure parameter or option

Returns the status of the specified procedure parameter or option. Returns the value 1 if a value was specified for the option or parameter when the procedure was executed (always returns 1 for options which have been assigned default values), otherwise returns a 0.

 

 

%density(x) — Standard normal density function

Standard Normal density function.

 

 

%det(A) — Determinant of an array

Computes the determinant of a SYMMETRIC or \(N \times N\) RECTANGULAR matrix A.

 

 

%diag(A) — Create diagonal matrix from a 1–dimensional array

Creates a square diagonal matrix from a vector. A may be either a VECTOR or an \(N \times 1\) or \(1 \times N\) RECTANGULAR.

 

 

%digamma( x ) — Digamma function 

Returns the digamma function of x. The digamma is the derivative of \(\log {\rm{ }}\Gamma (x)\), and is usually denoted \(\psi (x)\).

 

 

%dims(A) — Dimensions of a matrix

Returns the number of rows and columns in an array, as a VECTOR of integers, with the number of rows in entry 1, and the number of columns in entry 2. See also %COLS, %ROWS and %SIZE.

 

 

%dlminit(A,SW,F,Z) — Generate initial conditions for a state-space DLM

This returns a full solution for the initial conditions for a state space model with the given input matrices. It returns a VECT[RECT] with first component being the (finite) covariance matrix, the second the mean, and the third the diffuse covariance matrix. %PSDINIT solves a more limited problem for strictly stationary transition matrix A.

 

 

%dlmgfroma(A) — Transforming a state-space DLM to stationarity

This analyzes a state transition matrix A from a state-space model and produces the “G” matrix which transforms the model to its stationary states.

 

 

%dmills(x) — Derivative of the inverse Mills’ ratio

Returns the derivative evaluated at x of the inverse Mills’ ratio for the normal (\(\phi {\rm{/}}\Phi \)). The inverse Mills’ ratio itself is computed by the %MILLS function.

 

 

%dmult(A,v) — Multiply columns of a matrix by vector elements

Returns the result of multiplying the columns of A by corresponding elements in VECTOR V.

 

 

%dnn(n) — Duplication matrix

Returns the "duplication matrix" which maps a vech (lower triangle) of an \(n \times n\) symmetric matrix to the equivalent vec of a full \(n \times n\) matrix by duplicating the lower triangle elements to the above diagonal locations. Note that this creates a matrix to do the mapping—it doesn't do the mapping itself. This was added with version 9.2.

 

 

%dnninv(n) — Inverse duplication matrix

Returns the (generalized) inverse of a duplication matrix which maps the vec of an \(n \times n\) matrix to the vech (lower triangle) of a symmetric matrix. Note that this creates a matrix to do the mapping—it doesn't do the mapping itself. This was added with version 9.2.
 

 

%do(i,n,m,expr) — Internal do loop

Loops over the expression beginning with \(i=n\) as long as \(i \le m\). See the descriptions of EWISE and DO for examples.

 

 

%dow(year,month,day) — Day of week from expanded date

Returns the day of the week (Monday=1 through Sunday=7) for the date given by year,month,day. 

 

 

%dot(A,B) — Dot product of two arrays

Returns the “dot” product of A and B.

 

 

%easter(year) — Returns date of (Western) Easter Holiday

Returns the date of the Easter holiday for year in the Western Christian tradition as a number of days after March 22 (the earliest possible Easter date).

 

 

%eigdecomp(S) — Eigen decomposition of a symmetric matrix

Returns a 2-vector of RECTANGULAR arrays giving an eigen decomposition of the symmetric array S. The first array returned is the \(N \times 1\) matrix of eigenvalues, and the second is the \(N \times N\) matrix of eigenvectors (in the columns, normalized to unit length).

 

 

%eqncoeffs(equation) — Coefficients of an equation

Returns a VECTOR with the current coefficients for the specified equation. You can refer to equations by their name or handle. Use 0 as the argument to get the coefficient vector from the most recent regression.
 

 

%eqncopy(equation) — Makes a copy of an equation

Returns a copy of an equation. This is useful if you might be redefining the original equation and need to make a copy of it as it currently exists. This was added with version 9.2.

 

 

%eqndepvar(equation) — Get dependent variable of an equation

Returns the SERIES handle of the dependent variable of the specified equation. Use 0 as the argument to get the dependent variable in the most recent regression.

 

 

%eqngetidentity(equation) — Returns setting of “identity” tag for an equation

This returns the value of the identity tag for the equation. It returns 1 if the equation is an identity, 0 if it is not.

 

 

%eqnhandle(equation) — Get “handle” of an equation

Returns the integer number (handle) which can be used to represent the equation.
 

 

%eqnlag(equation,lag) — Lags right hand side of an equation

Returns a copy of an equation with all right hand side variables lagged an additional lag periods.

 

 

%eqnlagpoly(equation,series) — Extract lag polynomial

Extracts the lag polynomial for the selected series from an equation. Equation can be an equation name or number. Use zero to refer to the most recent regression. This returns a polynomial as a VECTOR of dimension (n+1), where n is the degree of the lag polynomial. The form of the polynomial depends upon which variable is extracted.

 

 

%eqnprj(equation,t) — Compute projected values of an equation

Returns the projected (fitted) value of equation at time period t. Use 0 for equation to use the explanatory variables from the most recent regression. Use %EQNVALUE if you want the value given a set of coefficients that you supply rather than the current coefficient values of the equation.

 

 

%eqnreglabels(equation) — Get regressor labels for an equation

Returns a VECTOR[STRINGS] with the labels of the regressors (explanatory variables) in an equation, formatted as shown in regression output (e.g., series{lag} to show lags). Use 0 as the argument to get the labels for the most recent regression.

 

 

%eqnresid(equation,t) — Residual value of equation at entry t

Returns the residual value of the equation at entry t.

 

 

%eqnrvalue(equation,t,coeffs) — Residual of equation given coefficient vector

Returns the residual value of equation at entry t, given a set of coefficient values provided by the VECTOR coeffs.

 

 

%eqnserieslag(series,lag) — Create equation “bit”

Returns an EQUATION with the explanatory variable series{lag} with a coefficient of 1.0. This can be used in building or adjusting an equation.

 

 

%eqnsetcoeffs(equation,C) — Reset coefficients of an equation

This sets the coefficients of equation to the vector C.

 

 

%eqnsetidentity(equation,tag) — Set the “identity” tag of an equation

This sets the “identity” tag for equation. This determines whether or not the equation is treated as an identity. To turn on the tag and make the equation an identity, use the value 1 for tag. Use the value 0 to turn off the tag.

 

 

%eqnsetresids(equation,r) — Set the residuals for an equation

This sets the residuals for equation to be the series r.

 

 

%eqnsetvariance(equation,v) — Reset variance of an equation

This sets the residual variance of equation to the value v.
 

 

%eqnsize(equation) — Number of explanatory variables in equation

Returns the number of explanatory variables in equation.

 

 

%eqntable(equation) — List of variables/lags in an equation

Returns a RECTANGULAR[INTEGER] array listing the explanatory variables in equation. The array has dimensions 2 × number of explanatory variables. Row one lists the series numbers of the explanatory variables, row two lists the lags. Use 0 for equation to get the table of variables in the most recent regression.

 

 

%eqnvalue(equation,t,coeffs) — Value of an equation

Returns the value of the linear equation at time period t, given coefficients coeffs—a set of coefficients supplied as a VECTOR. Use 0 for equation to use the explanatory variables from the most recent regression. Use %EQNPRJ if you want the value of an equation given the current coefficient values of the equation rather than user-inputted values.

 

 

%eqnvariance(equation) — Variance of an equation

Returns the variance associated with an equation (generally the residual variance from when it is estimated.)

 

 

%eqnxvector(equation,t) — Extract an X(t) vector for an equation

Returns a VECTOR with the “X” variables from the equation for time period t. Use 0 for equation to pull the explanatory variables from the most recent regression.
 

 

%execpath() — Return path to RATS executable file

This returns the path to the directory containing the RATS executable file in use. This can be useful if you need to reference a subdirectory of that path (for compiling a procedure file, for example) or need to verify the location of the executable file.

 

 

exp(x),%exp(A) — Scalar or elementwise exponentiation function

For a scalar real x, exp(x) returns \({e^x}\).  For an array A, %exp(A) returns an array B, such that \({{\bf{B}}_{ij}} = \exp \left( {{{\bf{A}}_{ij}}} \right)\).

 

 

%factorial(x) — Factorial function

Returns the factorial \(x! = x(x - 1)(x - 2) \ldots 1\) or, more generally \(\Gamma \left( {x + 1} \right)\). Note that this very rapidly will overflow—in practice, you are generally better off arranging calculations to use %LNGAMMA(x+1) to compute \(\log x!\).

 

 

%file(fname) — Get I/O Unit from File Name

Returns an I/O unit for a given file name string. Note: function call or variable set equal to function call must be preceded by the & dereferencing character, which tells RATS to evaluate the contents of the argument, rather than treating it as a literal string. For example:

 

compute tempunit = %file("c:\myfiles\salesdata.xls")

data(unit=&tempunit),format=xls,org=col)
 

 

%fill(rows,cols,value) — Create constant matrix

Creates a matrix with dimensions rows by cols, with all elements set to value. See also %ones and %zeros.

 

 

fix(x) — Convert real to integer by truncation

Converts a real value to an integer value by eliminating the fractional part (not by rounding—use %round(x,n) for that). Note that RATS will not automatically convert reals to integers in an expression.

 

 

float(n) — Convert integer to real

Explicitly converts an integer to a real.

 

 

%floatingdate(y,m,dow,n) — Day of month for floating holiday

Returns the day of the month of the nth occurrence of the specified day of the week (dow, coded as Monday=1 to Sunday=7) in the year y, month m. Use a negative value of n to count from the end. %floatingdate(2010,11,4,4) is the fourth Thursday of November, 2010, while %floatingdate(2010,11,4,-1) is the final Thursday.

 

 

%frac(x) — Fractional part of a real number

Returns x–[x], where [x] is the first integer value less than x. For example, %frac(9.7) returns .7, %frac(‑9.7) returns .3.

 

 

%fractiles(A,F) — Compute fractiles (quantiles)

Returns a VECTOR with fractiles (quantiles) of the elements of the array A. The list of desired quantiles are provided by the VECTOR F.

 

 

%freqend() — Number of frequency ordinates

Returns the number of ordinates set by the FREQUENCY instruction.

 

 

%freqsize(n) — Compute recommended number of complex ordinates

Returns the recommended number of ordinates for a FREQUENCY instruction, for n actual data points.

 

 

%ftest(x,n,m) — F-test tail probability

Returns the tail probability for an F(n,m).

 

 

%gamma(x) — Gamma function

Returns the gamma function of x. See also %LNGAMMA.

 

 

%gammainc(x,a) — Incomplete gamma function

Returns the incomplete gamma function of x given parameter a.

 

 

%gedcdf(x,s)   — CDF of the GED distribution       

Returns the CDF of the GED (generalized error distribution) with shape s at x.

 

 

%getenv(name)   — Get environment string

For a given operating system environment variable name, this returns the associated environment string. Returns a blank string if the environment variable is not defined in the operating system.

 

 

%gevcdf(x,k,mu,sigma) — CDF of Generalized Extreme Value

Returns the cdf of the Generalized Extreme Value distribution, for tail index k, location parameter mu, and scale parameter sigma.

 

 

%ginv(A) — Generalized inverse of a Matrix

Computes the generalized (Moore-Penrose) inverse of \(\bf{A}\). This is a matrix \({{\bf{A}}^ + }\) which solves \({\bf{A}}{{\bf{A}}^ + }{\bf{A}} = {\bf{A}}\) and \({{\bf{A}}^ + }{\bf{A}}{{\bf{A}}^ + } = {{\bf{A}}^ + }\). \(\bf{A}\) does not have to be square—\({{\bf{A}}^ + }\) will have the same dimensions as \({{\bf{A'}}}\).

 

 

%girfmatrix(S) — Generalized IRF Shock Matrix

Returns the shock matrix generated from a SYMMETRIC matrix that will give the "Generalized" Impulse Response Function. Each column in the output is the column in the input divided by the square root of its diagonal element (which is that column would be if it were the first column in a Cholesky factor). S must be positive semi-definite. Note that this is not a factor of S, and should not be used as the basis for calculating the decomposition of variance. This was added with 10.0.

 

 

%gpcdf(x,k,mu,sigma) — CDF of generalized Pareto

Returns the CDF of the Generalized Pareto distribution, for tail index k, location parameter mu, and scale parameter sigma.

 

 

%grparm() — Get Current Graph Label Settings

Returns a VECT[INTEGER] identifying the current font and type size settings for graph labels. Used with the RECALL option on GRPARM.

 

 

%gsortho(A) — Gram-Schmidt orthonormalization

Returns a column-wise Gram-Schmidt orthonormalization of A
 

 

%iabs(n) — Integer absolute value

Returns the absolute value of the integer n.

 

 

%identity(n) — Create identity matrix

Creates an identity matrix with dimensions n × n.

 

 

%idiv(m,n) — Integer division

Integer m divided by integer n, returning an integer result. Any remainder is ignored.

 

 

%if(x,y,z) — Evaluate a conditional expression

Returns y if x is non‑zero, returns z if x is zero. x must be integer or real, but y and z can be any expressions as long as they are matching types. Often used in SET instructions with x as a logical expression (that is, if x is true, return y, otherwise return z). Example

 

set bigx = %if(x>=.5,1.0,-1.0)

 

 

%imag(z) — Imaginary part of complex number

Returns the imaginary part of a complex number z.

 

 

%imax(m,n) — Maximum of two integers

Returns the maximum of the two integer arguments.

 

 

%imin(m,n) — Minimum of two integers

Returns the minimum of the two integer arguments.

 

 

%index(V) — Sorting index for a VECTOR

Returns a VECTOR[INTEGERS] which gives the sorting index for the vector V; that is, a VECT[INT] such that V(%INDEX(V(i))) would sort V into increasing order.

 

 

%indiv(t) — Individual within a panel set

When a panel data CALENDAR is set, this returns the number of the individual of which entry t is a part.

 

 

%innerxx(A) — Inner cross product

Returns \(\bf{A}'\bf{A}\) for the matrix A. See also %OUTERXX.

 

 

%instlist() — List of instruments

Returns the current list of instruments as a regressor list (a VECTOR[INTEGER] array). %INSTTABLE returns the same information, but in the form of a \(2 \times n\) array.

 

 

%insttable() — Table of instruments

Returns the table (a \(2 \times n\) array of integers) for the current list of instruments. Each column in the return array represents one series{lag} pair, with the series in the first row and lag in the second.

 

 

%instxvector(t) — Extract an X(t) for the instrument set

Returns a VECTOR with the current instruments for time period t.

 

 

inv(A) — Inverse of a matrix

Returns the inverse of the non-singular matrix A. A can be SYMMETRIC or \(N \times N\) RECTANGULAR. See %GINV for generalized inverses.

 

 

%invchisqr(p,r) — Inverse chi-squared tail probability

Returns the argument x for which the tail probability of a chi-square distribution with r degrees of freedom is p. In particular, %chisqr(%invchisqr(p,r),r)=p

 

 

%invchisqrnc(p,r,nc) — Inverse CDF non-central chi-squared

Returns the argument x for which the CDF of a non-central chi-square distribution with r degrees of freedom and non-centrality nc is p. In particular, %chisqrnc(%invchisqrnc(p,r,nc),r,nc)=p

 

 

%invftest(p,n,m) — Inverse F-test tail probability

Returns the value x for which the tail probability of an F with n and m degrees of freedom is p. In particular, %ftest(%invftest(p,n,m),n,m)=p.

 

 

 

%invged(p,c) — Inverse CDF of GED

Returns the inverse CDF of the generalized error distribution (GED) with shape parameter c (and variance 1).

 

 

%invgev(p,k,mu,sigma) — Inverse CDF of Generalized Extreme Value

Returns the inverse CDF of the Generalized Extreme Value distribution, for probability p, tail index k, location parameter mu, and scale parameter sigma.

 

 

%invgp(p,k,mu,sigma) — Inverse CDF of the generalized Pareto

Returns the inverse CDF of the Generalized Pareto distribution, for probability p, tail index k, location parameter mu, and scale parameter sigma.

 

 

%invnormal(p) — Inverse normal distribution

Returns the x for which the CDF of a standard Normal distribution is p. In particular, %cdf(%invnormal(p))=p

 

 

%invtcdf(p,r) — Inverse CDF of the t distribution

Returns the inverse CDF of the t distribution, for the probability p and degrees of freedom r.

 

 

%invttest(p,r) — Inverse t test

Returns the x for which the two-tailed probability of a t distribution with r degrees of freedom is p. In particular, %ttest(%invttest(p,r),r)=p

 

 

%invztest(p) — Inverse two-tailed normal test

Returns the x for which the two-tailed probability of a Normal distribution is p. In particular, %ztest(%invztest(p))=p. This was added with RATS 10.0.

 

 

 

%irfflatten(irf) — Flatten Impulse Responses

Takes a RECT[SERIES] of impulse responses and "flattens" it into the proper form for saving as an element in the %%RESPONSES array. This was added with RATS 10.1.

 

 

 

%isimpson(X,F) — Numerical integral by Simpson’s Rule

Returns a numerical integral computed using Simpson’s Rule. X is the vector of grid points (which should be equally spaced in increasing order) and F is a corresponding vector of function values.

 

 

%itrapezoid(X,F) — Numerical integral by Trapezoidal Rule

Returns a numerical integral computed using the trapezoidal rule. X is the vector of grid points (in increasing order, not necessarily equally spaced) and F is a corresponding vector of function values.

 

 

%julian(e) — Number of days from Jan 1, 0001 C.E.

Returns the number of days from a (theoretical) Jan 1, 0001 to (the final day in) entry e in the current CALENDAR scheme. This is the RATS julian date.

 

 

%julianfromcoded(x,codeformat) — Translation of numerically coded date (10.0)

Returns the RATS julian date corresponding to the value x, where the date is coded numerically according to the string codeformat. For instance, if dates are coded as numbers with digits yyyymmdd, then you would use %julianfromcoded(x,"yyyymmdd").

 

 

%julianfromymd(y,m,d) — Julian date for specified date

Returns the RATS julian date (number of days since January 1st, 0001, acting as if the Gregorian calendar extends back) for the date y:m:d.

 

 

%keys(hash) — Get keys from hash table of strings

Hash variables are an aggregate variable type where the elements stored in the hash are referenced by character strings, or “keys”. This function returns a list of the keys (strings) stored in the hash variable. 

 

 

%knn(n) — Transposition operator

Returns the transposition operator which maps a vec of an \(n \times n\) matrix to vec of its transpose. Note that this creates a matrix to do the mapping—it doesn't do the mapping itself. This was added with version 9.2.
 

 

%kroneker(A,B) — Kroneker product of two arrays

Returns the Kroneker product of arrays A and B. For A(m,n) and B(p,q), this computes an \(mp \times nq\) matrix \({\bf{A}} \otimes {\bf{B}}\).

 

 

%kronid(A,B) — Kroneker identity function

Computes \(\left( {{\bf{A}} \otimes I} \right){\bf{B}}\). A must be a square matrix; the first dimension of B must be a multiple of the dimension of A.
 

 

%kronmult(A,B,C) — Specialized Kroneker multiplication

Computes \(\left( {{\bf{A}} \otimes {\bf{B}}} \right){\bf{C}}\) where \(\left( {{\bf{A}} \otimes {\bf{B}}} \right)\) is the Kroneker product of A and B.

 

 

%l(s) — Get label of a series

Returns the label of series with the name or handle s.

 

 

%label(variable) — Get label of a series or other variable

Returns the label attached to the specified variable (that is, the name of the specified series, equation, etc.). Unlike %L, if you use a series number, you must use a type modifier to tell RATS that you want the label of a series.

 

 

%left(s,n) — Left substring

Returns the leftmost n characters of the string s.

 

 

%lnbeta(a,b) — Natural log of the beta function

Returns the natural log of the beta function B(a,b).

 

 

%lngamma(x) — Natural log of the Gamma function

Returns the natural log of \(\Gamma (x)\).

 

 

%lnlogistic(x) — Natural log of the logistic CDF

Returns \(\log \left( {\exp (x)/(1 + \exp (x)} \right)\), that is, the log of the logistic CDF.

 

 

 

%lnn(n) — Elimination matrix

Returns the "elimination matrix" which maps a vec of an \(n \times n\) matrix to the equivalent vech (lower triangle) by eliminating the above diagonal elements. Note that this creates a matrix to do the mapping—it doesn't do the mapping itself. This was added with version 9.2.

 

 

%lnnx(n) — Elimination matrix for below diagonal

Returns the "elimination matrix" which maps a vec of an \(n \times n\) matrix to the equivalent vech (lower triangle) by eliminating the elements at and above the diagonal. Note that this creates a matrix to do the mapping—it doesn't do the mapping itself. This was added with version 9.2.

 

 

log(x),%log(A) — Natural log function

Returns the natural log. If applied to a matrix A, returns B such that \({{\bf{B}}_{ij}} = {\log _e}{{\bf{A}}_{ij}}\)

 

 

%logbetadensity(x,α,β) — Log Density of Beta distribution

Returns the log density of the beta density for x, given \(\alpha\) and \(\beta\).

 

 

%logcdf(v,x) — Natural log of the normal CDF

Returns \(log \,\Phi \left( {x/\sqrt v } \right)\) where v is the variance, and \(\Phi \) is the normal CDF.
 

 

%logconcdensity(\({\hat \Sigma }\),T) — Log concentrated MV normal density

Returns the log concentrated density for a (multivariate) normal with covariance matrix \({\hat \Sigma }\) and number of observations T:

 

\( - \frac{{Tk}}{2}\left( {\log (2\pi ) + 1} \right) - \frac{T}{2}\log \left| {\hat \Sigma } \right|\)

 

      

 

%logdensity(A,v) — Log multivariate normal density

Returns the log density for a (multivariate) normal with covariance matrix A evaluated at the deviations from mean of v:

 

\( - \frac{1}{2}\left( {k\log \pi  + \log \left| {\bf{A}} \right| + {\bf{v'}}{{\bf{A}}^{ - 1}}{\bf{v}}} \right)\)

      

 

%logdensitycv(\({\Sigma }\),\({\hat \Sigma }\),T) — Log multivariate normal density

Returns the log of multivariate normal density as a function of \({\Sigma }\),\({\hat \Sigma }\) , and the number of observations (T):

 

\( - \frac{{Tk}}{2}\log (2\pi ) - \frac{T}{2}\log \left| {\hat \Sigma } \right| - \frac{T}{2}{\Sigma ^{ - 1}}\hat \Sigma \)

 

 

%logdensitydiag(V,u) — Log multivariate normal density with diagonal covariance

Similar to %LOGDENSITY except that the covariance matrix is diagonal, and V is a vector with the diagonal elements.
 

 

%logdetxx(S) — Log determinant of a symmetric matrix

Returns \({\rm{log}}\left| {\bf{S}} \right|\) for a symmetric matrix S.

 

 

%logdirichlet(x,d) — Log Density of Dirichlet

Returns the log density of a Dirichlet density. x and d must have the same dimensions, the d’s must be positive, and the x’s must sum to one.
 

 

%loggammadensity(x,c,b) — Log Gamma density

Returns the log density evaluated at x, for a gamma distribution with shape parameter c and scale b.

 

 

%loggeddensity(x,c,v) — Log GED density

Returns the log density evaluated at x, for a GED (generalized error distribution) with shape parameter c and variance v. This can be used for either univariate or multivariate GED distributions. Note that the scale parameter for the distribution is determined indirectly from the shape and the variance.

 

 

%loggevdensity(x,k,mu,sigma) — Log GEV density

Returns the log of the density function for the Generalized Extreme Value distribution for x, given tail index k, location parameter mu, and scale parameter sigma.

 

 

%loggpdensity(x,k,mu,sigma) — Log General Pareto density

Returns the log of the density function for the generalized Pareto distribution for x, given tail index k, location parameter mu, and scale parameter sigma.

 

 

%loginvchisqrdensity(x,degrees,scale) — Log density of scaled inverse chi-squared

Returns the log density at x for the scaled inverse chi-squared with degrees of freedom degrees and scale value scale. This was added with version 9.1.

 

 

%loginvgammadensity(x,a,b) — Log density of inverse gamma

Returns the log density at x for the inverse gamma with shape a and scale b. This was added with version 9.1.

 

 

%logistic(x,b) — Logistic function

Returns the logistic function: \(1/\left( {1 + b{e^{ - x}}} \right)\). This is “safeguarded” to avoid overflows.

 

 

%lognegbin(x,r,p) — Log of the negative binomial density

Returns the log of the negative binomial density of x given r and p.

 

 

%logpoissonk(mean,k) — Log of Poisson probability

Returns the log of \(P(x = k|m = mean)\) for a Poisson process with the mean given by mean.

 

 

%logtdensity(V,U,nu) — Log Multivariate t density

Returns the log of the multivariate t-density with nu degrees of freedom and covariance matrix V, evaluated at the vector of deviations from the mean U. Note that V is the covariance matrix of the t distribution itself, not of the underlying multivariate Normal on which it is based.

 

 

%logtdensitystd(V,U,nu) — Log Multivariate t density

Returns the log of the standardized multivariate t-density with nu degrees of freedom and covariance matrix V, evaluated at the vector of deviations from the mean U. This is equivalent to: %logtdensity(v*nu/(nu-2),u,nu)

 

 

%ltinv(L) — Lower triangular inverse

For a packed matrix L, this returns the inverse of the lower-triangular portion.

 

 

%ltouterxx(L) — Lower triangular outer product

For a packed matrix L, this returns the SYMMETRIC \(\mathbf{L}\mathbf{L}'\)

 

 

%matpeek(A,coords) — Extracting entries from a sparse matrix

Returns a VECTOR formed from extracting from the matrix A the row,column elements from the \(2 \times m\) RECT[INTEGER] coords in the matrix A.
 

 

%matpoke(A,coords,v) — Filling entries in a sparse matrix

Copies data from the VECTOR v (dimension m) to the row,column pairs elements specified by the \(2 \times m\) RECT[INTEGER] coords. The remaining entries of A are unaffected.

 

 

%max(x,y) — Maximum of two reals

Returns the maximum of two real values, x and y.

 

 

%maxindex(V) — Location of maximum value in a VECTOR

Returns the element number at which the maximum value of a VECTOR is attained.
 

 

%maxvalue(A) — Get maximum value of an array

Returns the maximum value of the array A. Use %minvalue to get the minimum value.

 

 

%mid(s,m,n) — Middle substring

Returns the n characters from the string s starting at position m. (Count positions beginning at 1). If \(n \le 0\), all characters from position m on are included.

 

 

%mills(x) — Inverse Mills’ ratio

Returns the inverse Mills’ ratio for a normal (\(\phi /\Phi \)) evaluated at x.

 

 

%min(x,y) — Minimum of two reals

Returns the minimum of two real values, x and y.       

 

 

%minimalrep(A,w) — Determines “minimal” representation

Returns a string giving a “picture” code for use by PRINT, DISPLAY or other output instructions which provides the “minimal” representation for the elements of A using at most w positions. This will be shorter than the representation given by %BESTREP if all elements of A can be shown to their full precision with only a few decimal places.

 

 

%minindex(V) — Location of minimum value in a VECTOR

Returns the element number at which the minimum value of a VECTOR is attained.

 

 

%minus(A) — Negative (“minus”) values of an array

Returns negative elements of array, with positive values replaced with zeros: \({{\bf{B}}_{ij}} = \min ({{\bf{A}}_{ij}},0)\). %plus is the similar function which takes plus values.

 

 

%minvalue(A) — Get minimum value of an array

Returns the minimum value of the array A. Use %maxvalue to get the maximum value.

 

 

%mod(m,n) — Modulo arithmetic

Returns the remainder from dividing m by n (integer arithmetic). See also %CLOCK(m,n) which does modulo arithmetic but returns values between 1 and n.

 

 

%modelalpha(M) — Error correction loadings for a MODEL

Returns the matrix of loadings on the error correction terms in a model that includes them. This was added with version 9.2.
 

 

%modelcompanion(M) — Companion matrix for a MODEL

Returns the companion matrix for a model.  The model must only include linear equations—the function will not work if the model includes non-linear formulas.

 

 

%modeldepvars(M) — Get dependent variables from a MODEL

Returns a VECTOR[INTEGER] which gives the series handles for the dependent variables of the equations or formulas in a model.
 

 

%modeleqn(M,n) — Get equation from a MODEL

Returns a copy of the equation at position n in model M.

 

 

%modelfind(M,s) — Locate an equation in a MODEL

Returns the position in model M of the equation or formula which has the series s as its dependent variable. Returns 0 if there is none.
 

 

%modelgetcoeffs(M) — Get coefficients from a MODEL

Returns a RECTANGULAR with the coefficients from the equations of model M. Each column of the output array will have the coefficients from a different equation.
 

 

%modelgetvcv(M) — Get covariance matrix from a MODEL

Retrieves the covariance matrix stored with model M.

 

 

%modellagmatrix(M,k) — Lagged Dependent Variable Coefficents for a MODEL

This returns the \(N \times N\) matrix of the coefficients for lag k of the dependent variables of model M (usually a VAR model). If the model has error correction terms, this returns the coefficients on the lagged differences in the error correction form.

 

 

%modellagsums(M) — Lag sums for a VAR MODEL

Computes the lag sums for a VAR model M. This is the matrix \(I - \sum\limits_{s = 1}^p {{\Phi _s}} \)  where \({{\Phi _s}}\) is the matrix of VAR coefficients for lag s. For a model with error correction terms, it returns the lag sums for the differenced variables in the error correction form.

 

 

%modellabel(M,i) — Label of dependent variable in a MODEL

Returns the label of the dependent variable of the equation or formula at position i in model M.

 

 

%modellargestroot(M) — Dominant root of MODEL

Returns the absolute value of the largest root of the companion matrix of model M.

 

 

%modelpoke(M,i,equation) — Replace an equation in a MODEL

This replaces the equation at position i in model M with equation.
 

 

%modelsetcoeffs(M,C) — Set coefficients from a MODEL

Sets the coefficients of (all the) equations of a model M. The coefficients are taken from the array C, with the coefficients for equation i in the model being taken from column i of C.

 

 

%modelsetvcv(M,S) — Set covariance matrix of a MODEL

Sets S as the residual covariance matrix of model M.
 

 

%modelsize(M) — Number of equations in a MODEL

Returns the number of equations or formulas in model M.
 

 

%modelsubstect(M) — Substitute out error correction terms in MODEL

Substitutes the error-correction terms out of model M, producing a model written in terms of the original variables only.

 

 

%month(e) — Month number (1–12) of entry e

Returns the month corresponding to entry e in the current CALENDAR scheme, where 1 is January, 2 is February, etc.
 

 

%mqform(A,B) — Matrix quadratic form operation

Returns \({\bf{B'AB}}\).

 

 

%mqformdiag(A,B) — Diagonal of matrix quadratic form

Returns a VECTOR containing the diagonal elements of \({\bf{B'AB}}\).

 

 

%mscalar(x) — Create a scalar matrix

Creates a scalar matrix equal to the identity matrix times the value x. You can only use this in an expression such as A=%MSCALAR(x), where \(\bf{A}\) is an \(N \times N\) matrix which has already been declared and dimensioned.

 

 

%mspexpand(P) — Markov switching probability function reparameterization

Takes the reduced size \((N−1) \times N\) matrix of Markov switching transition probabilities P (parameterized that way for estimation purposes) and expands it to a full \(N \times N\) matrix. This is the inverse of %MSPREDUCE.

 

 

%mspreduce(P) — Markov switching probability function reparameterization

Takes a full size \(N \times N\)  matrix of Markov switching transition probabilities P and reduces it to the \((N−1) \times N\) matrix of free parameters. This is the inverse of %MSPEXPAND.

 

 

%negbin(x,r,p) — Negative binomial density

Returns the negative binomial density (generalized to real-valued parameters).

 

 

%noprec(x) — Tests for loss of precision

Returns 1 or 0 depending upon whether x is “machine-zero”.
 

 

%normsqr(A) — Squared norm of a matrix

Returns the sum of squared elements of A.

 

 

%nullspace(A) — Orthonormal basis for null space

Returns an orthonormal matrix \(\bf{A}^ \bot \) which forms a basis for the null space of A. %NULLSPACE is similar to %PERP, but it does not assume that the input matrix has full rank in its smaller dimension. As a result, the dimensions of the output matrix will depend upon the rank of A, not just upon its dimensions.

 

%nyblomtest(x,p) — Nyblom fluctuations distribution

Returns the (approximate) tail probability at x of a standard Nyblom (1989) fluctuations test with p components. This is computed using a saddlepoint approximation, and should be quite accurate in the tails.
 

 

%ones(rows,cols) — Create a matrix of ones

Returns a matrix with dimensions rows × cols , with all elements equal to one.

 

 

%outerxx(A) — Outer cross product

Returns \({\bf{AA'}}\)  for the matrix A. Use %INNERXX(A) to get \({\bf{A'A}}\).
 

 

%ovcheck(x) — Checks for potential overflow

Returns a missing value if x is so large as to probably be the result of an unstable calculation. This will typically force the parameters generating a function evaluation to be rejected as out-of-range. If x is a “normal” number, %OVCHECK returns x.

 

 

%panelobs( ) — Size of panel data time dimension

Returns the number of periods per individual for panel data as was set on the CALENDAR instruction.
 

 

%panelsize() — Number of Individuals in Panel Set

Returns the number of individuals given the current CALENDAR(PANELOBS=...) setting and total number of observations. %PANELOBS() gives the number of time periods.

 

 

%parmset( ) — Returns the default PARMSET

This returns the current default parameter set.         

 

 

%parmslabels(P) — Extract parameters from a PARMSET

Returns a VECTOR[STRINGS] with the labels of the variables in parameter set P.       
 

 

%parmspeek(P) — Extract parameters from a PARMSET

Returns the parameters from PARMSET P as a VECTOR.       

 

 

%parmspoke(P,v) — Put vector into a PARMSET

Resets the parameters in PARMSET P from the vector v.       

 

 

%patchmat(Base,Source) — Replace NA’s in a matrix

Returns the matrix formed by patching over (replacing) any NA’s in the Base matrix with the corresponding entries from the Source matrix. Base and Source must have conforming dimensions.       

 

 

%patchzero(Base) — Replace NA’s in a matrix with zeros

Returns the matrix formed by patching over (replacing) any NA’s in the Base matrix with zeros.
 

 

%payment(a,r,n) — Required payments for an annuity

Returns the required payment for an annuity with principal a, interest rate r, and term n (a, r, and n are real values).

 

 

%period(e) — Period within a panel set

For entry e in the current CALENDAR scheme returns the time period within either the individual (for panel data) or the day (for intra‑day data), or year for other date schemes.

 

 

%perp(A) — Perp operator

Returns an orthonormal matrix \({{\bf{A}}^ \bot }\) which forms a basis for the null space of \({\bf{A}}\). If \(m > n\) (that is, \({\bf{A}}\) has more rows than columns), this is a basis for the left null space, so \({{\bf{A}}^ \bot }^\prime {\bf{A}}{\rm{ = 0}}\). \({{\bf{A}}^ \bot }\) is \(m \times (m - n)\). If \(m < n\), it will be a basis for the right null space, \({\bf{A}}{{\bf{A}}^ \bot } = 0\), with \({{\bf{A}}^ \bot }\)  being \(n \times (n - m)\).

 

 

%plus(A) — Non-negative (“plus”) values of an array

Returns positive elements of array, with negative values replaced with zeros: \({B_{ij}} = \max ({A_{ij}},0)\). Use %minus to get the minus version.
 

 

%poisson(mean,k) — Cumulative Poisson probability

Returns \(P(x \le {\rm{k}}|\mu  = {\rm{mean}})\) for a Poisson process with mean given by mean.

 

 

 

%poissonk(mean,k) — Poisson probability

Returns \(P(x = {\rm{k}}|\mu  = {\rm{mean}})\) for a Poisson process with mean given by mean.

 

 

%polyadd(V1,V2) — Add two polynomials

Adds two polynomials, represented by the vectors V1 and V2, where an n+1 vector V represents an n-degree polynomial, in the form \({\bf{V}}{\rm{(1) + }}{\bf{V}}{\rm{(2)}}{x^1}{\rm{ + }} \ldots {\rm{ + }}{\bf{V}}{\rm{(n + 1)}}{x^n}\).

 

 

%polycxroots(V) — Complex roots of a polynomial

Returns all roots of a polynomial represented as described under %POLYADD.

 

 

%polydiv(V1,V2,d) — Divide two polynomials

Divides polynomial V1 by polynomial V2 (where V1 and V2 are represented by VECTORS) up to degree d.

 

 

%polymult(V1,V2) — Multiply two polynomials

Multiplies two polynomials, represented by the vectors V1 and V2.

 

 

%polyroots(V) — Roots of a polynomial

Returns all real roots of a polynomial represented by the vector V.

 

 

%polysub(V1,V2) — Subtract two polynomials

Subtracts two polynomials, represented by the vectors V1 and V2.

 

 

%polyvalue(V,x) — Evaluate a polynomial

Returns the value of a polynomial (represented by the vector V) for a given value of x.

 

 

%psddiag(S,B) — Diagonalizing a symmetric matrix

For the positive semi-definite SYMMETRIC S, returns a lower triangular matrix L such that \({\bf{LSL'}}\) is diagonal with 1’s and 0’s on the diagonal. B is used to determine when a calculation has produced a zero (to machine precision). If S is full rank, %PSDDIAG(S,B) will give \({\bf{LSL'}} = {\bf{I}}\).

 

%psdfactor(A,IX) — Factoring symmetric matrix

Returns the Cholesky factor of the positive semi-definite SYMMETRIC A with ordering given by the index list in the VECTOR[INTEGER]IX. The function %DECOMP(A) is equivalent to %PSDFACTOR(A,||1,2,...,n||)

 

 

%psdinit(A,W) — Stationary covariance matrix

Returns a SYMMETRIC matrix V such that \({\bf{AVA'}} + {\bf{W}} = {\bf{V}}\). This is the stationary covariance matrix for a state-space model. %DLMINIT can solve a generalized problem with unit roots in the transition matrix A.

 

 

%psubmat(A,startrow,startcol,B) — Copy values into an array

Copies information in matrix B into matrix A, starting at (startrow,startcol) of A. Copied values overwrite any existing values in the affected entries of A. A must be sufficiently large to allow all entries in B to be copied into existing dimensions of A.

 

 

%psubvec(VA,position,VB) — Copy values into a vector

Puts the information in vector VB into vector VA, beginning at entry position of VA. The copied values will overwrite any existing values in the affected entries of VA. Note that VA must be sufficiently large enough to allow all entries of VB to be copied into the existing dimensions of VA.

 

 

%pt(V,t,X) — Filling a matrix of series

V is an array of SERIES, X should be an array of reals of the same size and shape. The elements at entry t of the series in V are filled with the corresponding values of vector X.

 

 

%qform(A,B) — Evaluate a quadratic form

Returns \({\bf{B'AB}}\), where B is either a VECTOR or an \(N \times 1\) or \(1 \times N\) RECTANGULAR array.

 

 

%qformd(A,B) — Evaluate a quadratic form with a diagonal matrix

Returns \(\sum\limits_i {{A_i}B_i^2} \) where A and B are either conforming VECTORS or \(N \times 1\) or \(1 \times N\) RECTANGULAR arrays.

 

 

%qformdpdf(D,x) — PDF of a diagonal quadratic form

Returns \(P({\bf{e'De}} < x)\) where D is a diagonal matrix (represented by a VECTOR).

 

 

%qforminv(S,v) — Inverse quadratic form

Returns  \({\rm{v'}}{{\rm{S}}^{ - 1}}{\rm{v}}\)where S is positive semi-definite symmetric.

 

 

%qformpdf(A,x) — PDF of a quadratic form

Computes \(P({\bf{e'Ae}} < x)\) for a quadratic form in Normal(0,1) variables, where A is SYMMETRIC and e is i.i.d. This can be used for ratios of quadratic forms as well, since \(P({\bf{eAe}}/{\bf{eBe}} < x) = P({\bf{e'}}({\bf{A}} - x{\bf{B}}){\bf{e}} < 0)\).

 

 

%qrdecomp(A) — QR decomposition

Returns a VECTOR[RECTANGULAR] with two elements, the Q and R, respectively, of \({\bf{QR}} = {\bf{A}}\), where Q is orthonormal (\({\bf{QQ'}} = I\)) and R is upper triangular.

 

 

%ran(x) — Random normal draw

Returns draws from a Normal distribution with mean zero and standard deviation x. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RAN(1.0)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value.

 

%ranbeta(a,b) — Random beta draw

Returns draws from a Beta distribution with shape parameters a and b. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANBETA(3.0,5.0)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value.

 

 

%ranbranch(P) — Random selection of a branch

Returns a random integer from {1,..,dim(P)} where the elements of P are the (unscaled) probabilities of the choices.
 

 

%ranchisqr(nu) — Random chi-squared draw

Returns draws from a chi-squared distribution with nu degrees of freedom. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANCHISQR(10)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value.

 

 

%rancombo(n,k) — Random combination

Returns a VECTOR[INTEGER] which is a random combination (draw without replacement) of k items from {1,...,n}.

 

 

%randirichlet(C) — Random Dirichlet

Returns a draw from a Dirichlet distribution. The Dirichlet is a generalization of the beta distribution. C is an n-vector of positive shape parameters. The return is an n-vector of probabilities (positive values summing to one).

 

 

%ranflip(p) — Random draw from Bernoulli distribution

Returns random draws (zeros or ones) from a Bernoulli distribution with probability p. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANFLIP(0.6)), this will fill all elements of the array with random draws. Otherwise, it returns a single draw.

 

%rangamma(r) — Random gammas

Returns draws from a gamma distribution with shape parameter r. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANGAMMA(10.0)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value.

 

%rangrid(X,F) — Random draw from approximate distribution

Returns a random draw from a distribution approximated by the grid. X is the vector of grid points (in increasing order, not necessarily equally spaced) and F is a corresponding vector of (relative) densities.

 

%raninteger(l,u) — Random integer

Returns an integer drawn randomly from \([l,u]\).

 

%ranks(A) — Ranks of the elements of an array

Returns an array with the same size and type as A with the ranks of the corresponding elements of A. Ranks are in increasing order beginning with 1. Ties are assigned the average of the covered ranks.

 

%ranlogkernel() — Log kernel density from recent draw

Returns the log kernel density from the most recent draw of random numbers.

 

%ranlognormal(mean,sd) — Draws from log Normal density

Returns draws from a log Normal distribution with mean mean and standard deviation sd. (Note that these are moments of the log Normal itself, not of the underlying Normal density). If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANLOGNORMAL(1.0,0.5)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value. This was added with Version 9.1.

 

%ranmat(m,n) — Rectangular matrix of random normal draws

Returns an \(m \times n\) matrix of random draws from a standard Normal(0,1) distribution.

 

 

%ranmvkron(FS,FX) — Draw from multivariate Normal regression

Returns a draw from a multivariate Normal regression. Inputs are a factor of the regression \(\Sigma\) matrix (FS) and a factor of the \({\left( {{\bf{X'X}}} \right)^{ - 1}}\) matrix (FX).

 

%ranmvkroncmom(C,H,P,M) — MV normal regression, CMOM variant

Returns a draw from a multivariate Normal regression given a cross-moment matrix C,  regression precision matrix (H), prior precision matrix (P) and prior mean (M).

 

%ranmvnormal(F) — Draw from random multivariate Normal

Returns a draw from a multivariate Normal with mean 0 and covariance matrix \({\bf{FF'}}\), that is, the argument provides a factor of the covariance matrix.

 

%ranmvpost(P1,M1,P2,M2) — Draw from a MV Normal posterior

Returns a draw from a multivariate Normal posterior combining multivariate Normals, with the given precisions (P1 and P2) and means (M1 and M2).

 

%ranmvpostcmom(C,h,P,M) — MV Normal posterior, CMOM variant

Returns a draw from a multivariate Normal posterior combining multivariate Normals, given a cross-moment matrix C, a regression precision (h), prior precision matrix (P) and prior mean (M).

 

%ranmvposthb(H,Hb) — Draw from a MV Normal posterior

Returns a draw from a multivariate Normal posterior given precision matrix H and precision times mean vector Hb. (In many applications, it's easier to compute Hb than the mean itself).

 

%ranmvt(F,nu) — Random draw from multivariate t

Returns a random draw from a multivariate t distribution, where nu is the degrees of freedom and F is a factor of the covariance matrix (the covariance matrix is \({\bf{FF'}}\)).

 

%ranpermute(n) — Random permutation

Returns a VECTOR[INTEGER] which is a random permutation (reordering) of {1,...,n}.

 

%ransign() — Random sign

Returns random signs (only values +1 and -1) drawn with equal probability. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANSIGN(10.0)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value.

 

%ransphere(n) — Random draw on the unit sphere

Returns a draw made uniformly from the unit sphere in n dimensions.

 

%ransvksc(u,mean,var) — Draws for log variance in stochastic volatility model

Returns a draw from the posterior for the log variance generated by combining a normal on the log variance (from adjoining observations) with an inverse gamma of the variance itself (from the observation). This is a step in a Gibbs sampling algorithm where the variance is drawn for a specific entry conditional on the variances at all other entries. It is based upon the rejection method of Kim, Shepard and Chib(1998) with refinements to provide better behavior. u is the residual, assumed to be distributed N(0,h). Conditioning on adjacent observations gives a Normal distribution for log h, where mean is the mean and var is the variance of that distribution. Note that these are moments of the log Normal, not of the underlying Normal density, and note again that it returns a draw for the log of the variance. This was added with Version 9.1.

 

%rant(d) — Random draw from Student t distribution

Returns a random draw from a t distribution with d degrees of freedom.

 

%rantruncate(mu,sig,lower,upper) — Random draw from truncated Normal

Returns a draw from a Normal with mean mu and standard deviation sig truncated to the interval [lower,upper]. lower or upper can be %NA to indicate an interval unbounded in that direction. If you use this in an expression where the left side of the expression is an array that has already been declared and dimensioned (A=%RANTRUNCATE(...)), this will fill all elements of the array with random draws. Otherwise, it returns a single real value.

 

%ranwishart(n,r) — Random Wishart matrix

Returns a draw from a \(n \times n\) Wishart distribution with identity covariance matrix and shape parameter r.

 

%ranwishartf(F,r) — Random Wishart with given covariance matrix

Returns a draw from a Wishart distribution with covariance matrix \({\bf{F'F}}\) and shape parameter r.
 

 

%ranwisharti(F,r) — Random inverse Wishart

Returns a draw from an inverse Wishart distribution with covariance matrix \({\bf{F'F}}\) and shape parameter r.
 

 

%ratsversion() — Get version number of RATS

This returns the version number of the copy of RATS you are using.

 

 

%real(z) — Get real part of complex number

Returns the real part of a complex number z.

 

 

%regend() — Return regression ending entry

Returns the ending entry/date of the most recently completed regression or estimation.

 

 

%reglabels() — Get regression labels

Returns a VECTOR[STRINGS] with the output labels from the regressors or non-linear parameters from the most recent estimation.

 

 

%reglist() — Get regressor list

Returns the regressor list from the most recent regression as a coded VECT[INTEGER]. You can use %RLADDONE and related functions to modify the regressor list.

 

 

%regload(R) — Reload saved regression

Loads into memory from R a regression saved using %REGSAVE(). Subsequent instructions such as TEST, other hypothesis test operations, and PRJ will apply to this regression.
 

 

%regsave() — Save a regression

Saves the most recent regression, as a coded VECT[INTEGER].

 

%regsetrange(start,end) — Reset regression range information

Sets the recoverable regression range (used by %REGSTART() and %REGEND()) to the start and end values.

 

%regstart() — Return regression starting entry

Returns the starting entry/date of the most recently completed regression or estimation.
 

 

%regtable() — Returns the "table" for the most recent regression

Returns a RECTANGULAR[INTEGER] array listing the explanatory variables in the most recent regression. The array has dimensions 2 × number of explanatory variables. Row one lists the series numbers of the explanatory variables, row two lists the lags. Use 0 for equation to get the table of variables in the most recent regression.

 

 

%reshape(A,r,c) — Change the dimensions of an array

Returns the contents of A with dimensions changed  (usually from rectangular to vector or vice versa). r and c provide the number of rows and columns, respectively, in the new array. See also %VEC and %VECTORECT.

 

 

%right(s,n) — Right substring

Returns the rightmost n characters from the string s. Use the %MID function to get the rightmost characters from a known position within the string.

 

 

%rladdlag(R,S,L) — Add a lagged regressor to a regressor list

Adds lag L of series S to an existing regressor list R. See also %RLADDONE.

 

 

%rladdlaglist(R,S,list) — Add list of lags to a regressor list

Adds the lags included in list for series S to regressor list R. This is identical to %RLADDLAG(), except list is a list of lag numbers (as a VECT[INTEGER]), rather than a single lag.
 

 

%rladdone(R,S) — Add a regressor to a regressor list

Adds a series S (unlagged) to existing regressor list R.

 

 

%rlconcat(R1,R2) — Concatenate two regressor lists

Concatenates two regressor lists into a single list.
 

 

%rlcount(R) — Number of regressors in list

Returns the total number of variables in a regressor list once lag fields are expanded.

 

 

%rlempty( ) — Empty Regressor List

Returns an empty regressor list; this is identical to a VEC[INT] with dimension 0.
 

 

%rlfromeqn(eqn) — Get a regressor list from an equation

Returns the regressor list from created from the explanatory variables in EQUATIONeqn.

 

 

%rlfromtable(table) — Get a regressor list from a regression table

Returns a regressor list from a regression table (such as generated by %EQNTABLE or %INSTTABLE).
 

 

%rlverify(R) — Verify a regressor list

Verifies that R forms a valid regressor list. Useful when creating your own regressor lists or modifying existing regressor lists.

 

 

%round(x,n) — Rounding

Returns x rounded to n decimal places. Negative values of n round to positive powers of 10, that is, %round(1536,-2)=1500.

 

 

%rows(A) — Number of rows in a matrix

Returns the number of rows in a matrix A.
 

 

%rsscmom(C,V) — Residual sum of squares from a cross product

This returns the residual sum of squares given a (properly structured) cross moment matrix C and a coefficient vector V. 

 

 

%s(L) — Series from label

Returns the series handle for the series whose name is the label L. If such a series doesn’t yet exist, it will be created. For instance,

 

SET %S("TREND"+I) = T^I

 

will, if I is 2, create series TREND2 as a squared trend. 

 

 

%scalar(A) — Get first element of a matrix

Returns A(1,1) (or A(1) for a VECTOR).

 

 

%scol(S,col) — Series from Column in Array of Series

Returns a VECTOR[INTEGER] with the series handles for a column of a matrix of SERIES.

 

 

%sec(x) — Secant function

Returns the secant of x.

 

 

%selseries() — Return series selected in the Series List  

Returns a VECT[INTEGER] with the handles of the series currently selected in the Series List window.

 

 

%seq(m,n) — Creates an Integer Sequence

Returns a VECTOR[INTEGER] with the sequence from m to n which can be in either order.

 

 

%seqa(start,incr,n) — Creates a Vector with a Real-Valued Sequence

Returns a VECTOR of dimension n filled with the sequence starting with start and incremented by incr for each subsequent entry. See also %SEQRANGE.

 

 

%seqrange(lower,upper,n) — Creates a Vector with a Real-Valued Sequence

Returns a VECTOR of dimension n filled with a sequence of constant-magnitude increments from lower to upper. See also %SEQA.

 

 

%seriesentry(series,entry) —  Panel data series entry references

When working with panel data, references to a series entry in a SET or FRML command will return “NA” (missing value code) if the entry referenced is in a different individual than the entry being set or evaluated—this is done to prevent lag computations from “lagging across” individuals. If you want the actual value of the series entry, regardless of whether it is in the current individual, use %seriesentry(series,entry) rather than just series(entry).

 

 

%sigmacmom(C,B) — Sum of squared error matrix from cross product

This returns the matrix with the sum of squared multivariate errors from a multivariate regression (same explanatory variables in each), given a (properly structured) cross moment matrix C and a coefficient matrix B. 

 

 

%sign(x) — Sign function

Returns 1 if x is positive, –1 if it’s negative and 0 if it’s zero.

 

 

sin(x) — Sine function

Returns the sine of x, where x is in radians. If x is a matrix, transforms each element.

 

 

%sinh(x) — Hyperbolic sine

Returns the hyperbolic sine of its argument:\(\left( {\exp (x) - \exp ( - x)} \right)/2\)

 

 

%size(A) — Size of an array

Returns the total number of elements in an array

 

 

%skewnn(n) — Skew-symmetric mapping matrix

Returns a matrix operator which will maps the vech of an \((n - 1) \times (n - 1)\) lower triangle to the vec of an \(n \times n\) skew-symmetric matrix which has the lower triangle below its diagonal, and minus the transpose of the lower triangle above its diagonal. Note that this creates a matrix to do the mapping—it doesn't do the mapping itself. This was added with version 9.2.

 

 

%slike(template) — Series Handles by Template

Returns a VECT[INTEGER] of the series handles matching a name template.

 

 

%solve(A,b) — Solves linear equations

Returns solution x of Ax = b.  A is an \(N \times N\) real matrix, b is an N-element vector.

 

 

%sort(A) — Sorts an array

Returns an array which has the same size and shape as A, but with the elements of A sorted in increasing order. If A is RECTANGULAR, the sorted values are stored by columns.

 

 

%sortc(A,c) — Sort on a column

Returns a copy of array A sorted based upon the values in column c. This normally sorts in increasing order. Make c negative to sort on a column in decreasing order.

 

 

%sortcl(A,list) — Sort on multiple columns

Returns a copy of array A sorted on the values of the columns in the list. list should be a VECTOR[INTEGER], or an “in-line matrix” of the form ||col1,...,coln||. The first column listed is the primary key, the others are used in order to break ties. Use the negative of a column number to have that column sort in decreasing order.

 

 

sqrt(x),%sqrt(A) — Square root function

Square root function. For %SQRT, this returns an array with the same dimensions and type as A with each element replaced by its square root. For SQRT, it's the square root.

 

 

%srow(S,row)  — Series from Row in Array of Series

Returns a VECTOR[INTEGER] with the series handles for a row of a matrix of SERIES.

 

 

%stereo(V) — Stereo projection

Returns the conversion of a general \(n-1\) element vector to an n vector on the unit sphere using the stereo projection.

 

 

%strcmp(s1,s2) — Compare two strings

Compares two strings. Returns 0 if they are identical, 1 if s1>s2 in lexicographical order, and –1 if s1<s2. Note that the return for equal strings is 0, not 1.
 

 

%strcmpnc(s1,s2) — Compare two strings disregarding case 

Compares two strings without regard to case. Returns 0 if they are identical, 1 if s1>s2 in lexicographical order, and –1 if s1<s2. Note that the return for equal strings is 0, not 1.

 

 

%strescape(s,chars,escape) - Escape special characters

Returns a copy of s with any character from chars escaped by prefixing with escape. For instance, %strescape("US$Exch","$","\") will return the string "US\$Exch"

 

 

%strfind(s,f) - Find substring

Searchs string s for string f, returning the position in s if found and zero otherwise.

 

 

%string(n) — Convert integer value to a string

Returns the character string corresponding to the integer n (for instance, %STRING(110) returns "110").

 

 

%strlen(s) — Returns the length of a string

Returns the length (number of characters) of the string s.

 

 

%strlower(s) — Convert string to lower case

Returns a copy of the string s with all characters in lower case.

 

 

%strmatch(s,pattern) — Test string for pattern match

Tests the string s for a match with pattern, returning 1 for a match and 0 for a failure to match. The pattern can include the following “wildcard” characters: * for matching 0 or more characters, ? for matching exactly one character, # for matching exactly one digit. Any other character must be an exact match (case is ignored for letters). For example, the pattern "*###" matches any string ending with three digits.
 

 

%strrep(s,n) — Repeats a string

Returns a string that consists of the input string s repeated n times.
 

 

%strtrim(s) — Trim a string

Returns a copy of a string with leading and trailing spaces and quotes removed.

 

 

%strupper(s) — Convert string to upper case

Returns a copy of the string s with all characters in upper case.

 

 

%strval(x,pc) — String showing a numerical value

This returns a string that displays the real value x in the picture code pc. For instance, %strval(11.9,"*.##") will return the string 11.90.

 

 

%sum(A) — Sum of array elements

Returns the sum of all elements in the array A. For SYMMETRIC arrays, it computes the sum of the lower triangle only. This can also be applied to SERIES variables, in which case the sum will be computed over the defined range of the series, or the range set by an SMPL instruction. Any missing observations will be omitted from the computation.

 

 

%sumc(A) — Sums columns of an array

This computes the sums of each column in an array. For an \(M \times N\) array, this returns an \(N \times 1\) array where element j contains the sum of all the elements in column j of the array A. Any missing observations will be omitted from the computation.

 

 

%sumr(A) — Sums rows of an array

This computes the sums of each row in an array. For an \(M \times N\) array, this returns an \(M \times 1\) array where element i contains the sum of all the elements in row i of the array A. Any missing observations will be omitted from the computation.

 

 

%svdecomp(A) — Singular Value Decomposition

Returns a VECTOR[RECTANGULAR] with three elements, the U, W and V, respectively, of \({\bf{A}} = {\bf{U}}[diag({\bf{W}})]{\bf{V'}}\), where U and V are column orthonormal, and W is the vector of diagonal elements in the SVD. The singular values will be sorted in descending order.

 

 

%sweep(A,k) — Sweep function of a matrix

Returns the result of sweeping matrix A on pivot k. A must be a square RECT or SYMM array. k is any integer from 1 to N. A is an \(N \times N\) matrix.

 

 

%sweeplist(A,list) — Sweep function of a matrix

Returns the result of sweeping matrix A on the pivots given by the VECTOR[INTEGER] list. The sweep function is described with %SWEEP.

 

 

%sweeptop(A,k) — Sweep function of a matrix

Returns the result of sweeping matrix A on all pivots 1,...,k. The sweep function is described under %SWEEP.

 

 

%symmcol(n) — Get column number from packed position

Returns the column number corresponding to element n in a packed symmetric or packed lower triangular matrix.
 

 

 

%symmpos(row,col)  — Get position of row,col in packed array

Returns the position in a packed symmetric or lower triangular matrix for a given row and column in the unpacked matrix.

 

 

%symmrow(n)  — Get row number from packed position

Returns the row number corresponding to element n in a packed symmetric matrix or lower triangular matrix.

 

 

%tablediff(table1,table2) — Find differences in tables

Finds the difference between two tables, returning a table with all variables from table1 which are not in table2.

 

 

%tableextract(table, list) — Extract subtable

Returns a subtable with the items in the listed positions of the argument table. list would usually be generated using %TABLEFINDALL or %TABLEFINDMISS.
 

 

%tablefind(table,series,lag) — Locate a single variable in a table

For series series and lag lag, this locates the requested variable (series{lag}) in regression table table. It returns the position of the variable, or zero if it’s not present.

 

 

%tablefindall(table1,table2) — Locate variables in a table

Locates in table1 the series,lag pairs from table2. It returns a VECTOR[INTEGER] with the positions of the regressors in table1 that also appeared in table2. 
 

 

%tablefindlags(table,s) — Locate lags of a series in a table

Returns the list of lags of series s which appear in table.

 

 

%tablefindmiss(table1,table2) — Locates variables missing from table

Returns a VECTOR[INTEGER] which shows the positions of variables in table1 that are not also in table2.

 

 

%tablefromrl(R) — Create table from regressor list

Creates a regressor table from a regressor list.

 

 

%tablemerge(table1,table2) — Merge two regressor tables

Merges two regression tables into a single regression table. Duplicates are included just once.

 

 

%tableunique(table) — Locate series in table

Returns a table which includes just one entry for each series which appears in table, showing only lag zero (no matter which lags appear in the table).

 

tan(x) — Tangent function

Returns the tangent of x, where x is in radians. If applied to a matrix, all elements are transformed.

 

 

%tanh(x) — Hyperbolic tangent

Returns the hyperbolic tangent of its argument:

 

\(\frac{{\exp (x) - \exp ( - x)}}{{\exp (x) + \exp ( - x)}}\)

 

 

%tcdf(x,d) — CDF for t distribution

Returns the CDF at x for a t distribution, with degrees of freedom d.

 

 

%tcdfnc(x,d,nc) — CDF for non-central t distribution

Returns the CDF at x for a non-central t distribution, with degrees of freedom d, and non-centrality parameter nc.

 

 

%tdensity(x,d) — t density

Returns the density function at x for a t distribution with d degrees of freedom.

 

 

%tdensitync(x,d,nc) — Non-central t density

Returns the density function at x for a non-central t distribution, with degrees of freedom d, and non-centrality parameter nc.

 

 

%testdiff(base,test) — Test difference of two arrays

Returns the convergence criterion used by the non-linear estimation instructions applied to the VECTOR's base and test. The formula is:

 

\(\mathop {\max }\limits_i \left\{ {\,\min \left[ {\left| {\frac{{tes{t_i} - bas{e_i}}}{{bas{e_i}}}} \right|,\left| {tes{t_i} - bas{e_i}} \right|} \right]} \right\}\)
 

 

%today() ­— Today’s entry

Returns the entry number in the current CALENDAR scheme which covers today’s date (that is, the system date of the computer at run time).

 

 

tr(A) — Transpose of a matrix

Returns the transpose of matrix A.

 

 

%trace(A) — Trace of a matrix

Returns the trace of a SYMMETRIC or \(N \times N\) matrix A.

 

 

%tradeday(e,dow) — Number of trading day occurrences

Returns the number of occurrences of weekday dow (Monday=1, Tuesday=2, …, Sunday=7) in entry e in the current CALENDAR scheme. For instance, January 2010 started on a Friday, and so has five of each of Friday, Saturday and Sunday, and four of the other days. With a monthly calendar, %TRADEDAY(2010:1,1) (number of Mondays) is 4 while %TRADEDAY(2010:1,5) (number of Fridays) is 5.

 

 

%trigamma(x) — Trigamma function

Returns the trigamma function of x. The trigamma is the second derivative of \(\log {\rm{ }}\Gamma (x)\), and is usually denoted \(\psi '(x)\). (\(\psi (x)\) is the digamma function).
 

 

%tsign(x,y) — Sign transfer

Returns \(\left| x \right|\) if y is positive, \(-\left| x \right|\) if y is negative, 0 if y is zero.

 

 

%ttest(x,r) — Two-tailed t test

Returns the two‑tailed probability of a t with r degrees of freedom, that is, the probability that a t-distributed random variable with r degrees of freedom exceeds x in absolute value.

 

 

%uniform(l,u) — Random draw from a uniform distribution

Returns a random draw from a uniform distribution ranging from (the real values) l to u. If you use this in an expression where the target of an assignment is an array (that is, something like A=%UNIFORM(0.0,1.0)), this will fill all elements of the array with (independent) random draws. Otherwise, it returns a single real value.

 

 

%unit(x) — Unit circle value

Returns the unit circle value \(\exp (ix)\).

 

 

%unit2(n,T) — Unit circle value for \(2\pi (n-1)/T\)

Returns the unit circle value \(\exp \left( {2\pi i(n - 1)/T} \right)\).

 

 

%unitfn(unit) — Get file name for I/O unit

Returns the filename associated with the I/O unit whose name is given by the string unit. For example, if you have done

 

open data mydata.xls

 

then %unitfn("data") would return "mydata.xls".

 

 

%unitfnext(unit) — Get extension of file name for I/O unit

Returns the extension (characters after the last period) of the filename associated with the I/O unit whose name is given by the string unit. For example, if you have done

open data mydata.xls

 

then %unitfnext("data") would return "xls".

 

 

%unitfnpath(unit) — Get path of file for I/O unit

Returns the path name (not including the filename) of the file associated with the I/O unit whose name is given by the string unit. For example, if you have done

 

open data c:\rats\projects\mydata.xls
 

then %unitfnpath("data") would return "c:\rats\projects".
 

 

%unitfnroot(unit) — Get root name of file for I/O unit

Returns the main part of the filename, not including the last period or any extension, for the file associated with the I/O unit whose name is given by the string unit. For example, if you have done

 

open data mydata.xls
 

then %unitfnroot("data") would return "mydata".

 

 

%unitv(n,i) — Generating a unit vector

This generates the ith unit n-vector—a vector with n elements, with element i set to one, and the other elements set to zero.

 

 

%valid( x ) — Check for valid (non-missing) value

Returns a value of 1 if and only if (all elements of) x are not the system missing value (%NA). In all other cases, it returns a zero. Use it to test for missing values. If applied to a matrix, all elements must be valid to get a 1 return value.
 

 

%value(s) — Value from string

Returns the value of a number coded into the string s. %value("13.5") is the real number 13.5.

 

 

%vec(A) — Vectorizing an array

Returns a VECTOR containing the values of array A. If A is RECTANGULAR, A is stripped out by columns; if SYMMETRIC or PACKED, by the rows of the lower triangle.

 

 

%vech(S) — Vectorizing a SYMMETRIC

Returns a VECTOR containing the values of array S. If S is SYMMETRIC or PACKED, the target is created by running through the the rows of the lower triangle. (This is actually the same as %VEC, but since stringing out a symmetric matrix by lower triangle is generally referred to as a "vech" operation, we've added a function by that name).

 

 

%vectorect(V,r) — Create a RECTANGULAR from a Vector

Reformats the values of the vector V into a RECTANGULAR with r rows. Elements 1 through r of V go into column 1 of the output array, elements r+1 through 2r go into column 2, and so on. This is the “inverse” of the %VEC function applied to a RECTANGULAR array with r rows.

 

 

%vectosymm(V,r) — Create a SYMMETRIC from a Vector

Reformats the values of the vector V into a SYMMETRIC with r rows, filling the symmetric array row by row. This is the “inverse” of the %VEC function applied to a SYMMETRIC with r rows.
 

 

%weekday(e) — Day of week of entry e

Returns the day of the week (1=Monday through 7=Sunday) of entry e in the current CALENDAR scheme.
 

 

 

%wfractiles(A,W,F) — Compute fractiles

Returns a VECTOR with fractiles (quantiles) of the elements of the array A with (un-normalized) weights provided by W. W needs to have the same shape as A. The list of desired fractiles are provided by the VECTOR F.

 

 

%xcol(A,i) — Extract column of a matrix

Extracts column i from matrix A.

 

 

%xdiag(A) — Extract diagonal from a matrix

Extracts the diagonal from matrix A.

 

 

%xrow(A,i) — Extract row

Extracts row i from matrix A.

 

 

%xsubmat(A,startrow,endrow,startcol,endcol) — Extract a matrix

This extracts an \(M \times N\) rectangular matrix from matrix A. For example, to extract the upper-left \(4 \times 4\) elements of A, you would use %xsubmat(A,1,4,1,4).

 

 

%xsubvec(V,startrow,endrow) — Extract a vector

Extracts elements startrow through endrow of vector V.

 

 

%xt(V,t) — Extract from an array of SERIES

From an array of SERIES, it extracts the entries t of the component series to form an array with the same size and shape as V.

 

 

%year(e) — Year number

Returns the calendar year corresponding to entry e in the current CALENDAR scheme.

 

 

%ymdaycount(y,m) — Number of days in specified year/month

Returns the number of days in month m of year y. For example, %ymdaycount(2012,9) returns 30: the number of days in September, 2012.
 

 

%ymddow(y,m,d) — Day of week for specified date

Returns the day of the the week (1=Monday,...,7=Sunday) for the date y:m:d. For example, %ymddow(2012,9,1) returns 6, as September 1st, 2012 is a Saturday.

 

 

%ymdjulian(y,m,d) — Julian date for specified date

Returns the Julian date (number of days since January 1st, 0001, acting as if the Gregorian calendar extends back) for the date y:m:d.

 

 

%zeros(rows,cols) — Create a zero matrix

Returns a matrix with dimensions rows × cols, with all elements equal to zero.

 

 

%zlag(t,x) — Transfer function for lag

Returns \(\exp \left( { - i2\pi (t - 1)x/N} \right)\) where N is the number of frequencies set on the FREQUENCY instruction. As t runs from 1 to N, this gives the appropriate Fourier transform for the lag operator \(L^x\).

 

 

%ztest(x) — Two-tailed standard normal probability

Returns the two‑tailed probability for Standard Normal, that is, the probability that a Normally distributed random variable exceeds x in absolute value.
 

 

Copyright © 2025 Thomas A. Doan