INITIAL Instruction

INITIAL( options ) equation start end

Computes initial estimates of an ARMA model specified with EQUATION. Use ITERATE to compute final estimates.

BOXJENK is the preferred way to estimate ARMA models—INITIAL is a holdover from earlier versions of RATS.

Parameters

equation	Equation whose initial estimates are to be computed.
start, end	Range of entries to use in computing the covariances needed for the calculation. If you have not set a SMPL, this defaults to the defined range of the dependent variable of equation.

Options

[PRINT]/NOPRINT

The output from INITIAL lists the variables, lags and initial estimates of the coefficients. You can suppress the output with NOPRINT.

COVARIANCES=series supplying autocovariances [unused]

Use the option COVARIANCES to solve for the ARMA representation of a process with a specific covariogram. The series of autocovariances should start with lag 0 (the variance) in entry 1 and should have at least as many lags as the highest AR lag plus the highest MA lag.

TRANSFER=source equation for coefficients [unused]

If you use TRANSFER, INITIAL does no calculations. It simply copies coefficients from source equation to equation. Any variables in equation which do not appear in source equation get zero coefficients.

Description

INITIAL computes initial estimates for the ARMA parameters of equation using the autocovariances of the dependent variable, or those provided by the COVARIANCES option. INITIAL uses the algorithms on pp. 223-224 of Box, Jenkins, and Reinsel (2008), using the linearly convergent (Gauss–Seidel) algorithm for the initial estimates of the moving average part. If the equation is an autoregression, this process produces solutions to the Yule-Walker equations.

There may be no solution to the system of equations used for the moving average part. For instance, no MA(1) model is compatible with a first lag correlation greater than .5. This failure usually indicates a poorly specified or overparameterized model. If RATS cannot solve the system of equations, it issues a warning, sets the estimate for the highest MA lag to zero and computes estimates for the remaining coefficients.

Example

equation(ar=2,ma=1) billeq tbills

initial billeq

iterate billeq