DURBINLEVINSON Procedure

@DurbinLevinson uses the Durbin-Levinson recursion to estimate the coefficients in a sequence of autoregressive representations for a stationary series.

@DurbinLevinson( options )series start end

Parameters

series	series to analyze
start, end	range of series to use. By default, the defined range of series.

Options

M=number of autoregressive coefficients

METHOD=[YULE]/BURG

Sets the method used for computing the covariances. If you use METHOD=BURG, you'll get the sequence of Burg AR estimates; if METHOD=YULE (default), they'll be the Yule-Walker AR estimates.

COVARIANCES=input series of covariances

If you don't use this, the covariances are computed using the input series. If you do use this, the series input is ignored.

PHI=(output) m x m matrix of autoregressive representations.

Row i has the AR(i) coefficients (thus row 1 will be one non-zero number followed by zeros).

V=(output) m vector of estimated residual variances

Element i has the residual variance for the AR(i)

Variables Defined

%BETA	coefficients in the final AR(m) (VECTOR)
%SIGMASQ	estimated residual variance for AR(m) (REAL)

Example

* Brockwell & Davis, Introduction to Time Series and Forecasting, 2nd ed.

* Example 5.1.1 from pp 143-144

open data dowj.dat

data(format=free,org=columns) 1 78 dowj

@bjident(diffs=1,number=30) dowj

set ddow = dowj-dowj{1}

* This does the Durbin-Levinson recursion for up to 3 lags

@durbinlevinson(m=3,phi=phi,v=v) ddow

* The matrix phi has the estimated autoregressions in the rows

disp "Durbin-Levinson Recursion Matrix"

disp phi

@arautolags(crit=caic,method=yule,max=27,table) ddow

Output

@DurbinLevinson displays no output itself. The example program displays the table of estimated AR's shown below. The first row is for an AR(1), the second for AR(2) and the last for the full AR(3).

Durbin-Levinson Recursion Matrix

0.42188 0.00000 0.00000

0.37388 0.11378 0.00000

0.37217 0.10817 0.01500