Language Reference: FARMAFIT Call :: SAS/IML(R) 9.22 User's Guide

Language Reference

FARMAFIT Call

CALL FARMAFIT( d, phi, theta, sigma, series <*>, p <*>, q <*>, opt ) ;

The FARMAFIT subroutine estimates the parameters of an ARFIMA( $\text{[math]}$ ) model.

The input arguments to the FARMAFIT subroutine are as follows:

series

specifies a time series (assuming mean zero).

p

specifies the set or subset of the AR order. If you do not specify p, the default is p $\text{[math]}$ .

If you specify p=3, the FARMAFIT subroutine estimates the coefficient of the lagged variable $\text{[math]}$ .

If you specify p= $\text{[math]}$ , the FARMAFIT subroutine estimates the coefficients of lagged variables $\text{[math]}$ , $\text{[math]}$ , and $\text{[math]}$ .

q

specifies the subset of the MA order. If you do not specify q, the default value is 0.

If you specify q=2, the FARMAFIT subroutine estimates the coefficient of the lagged variable $\text{[math]}$ .

If you specify q= $\text{[math]}$ , the FARMAFIT subroutine estimates the coefficients of lagged variables $\text{[math]}$ and $\text{[math]}$ .

opt

specifies the method of computing the log-likelihood function.

opt=0: requests the conditional sum of squares function. This is the default.
opt=1: requests the exact log-likelihood function. This option requires that the time series be stationary and invertible.

The FARMAFIT subroutine returns the following values:

d: is a scalar that contains a fractional differencing order.
phi: is a vector that contains the autoregressive coefficients.
theta: is a vector that contains the moving average coefficients.
sigma: is a scalar that contains a variance of the innovation series.

As an example, consider the following ARFIMA( $\text{[math]}$ ) model:

$\text{[math]}$

In this model, $\text{[math]}$ . The following statements estimate the parameters of this model:

d = 0.3;
phi = 0.5;
theta = -0.1;
call farmasim(yt, d, phi, theta);
call farmafit(d, ar, ma, sigma, yt) p=1 q=1;
print d ar ma sigma;

Figure 23.103 Parameter Estimates for a ARFIMA Model

d	ar	ma	sigma
0.2163452	0.4384969	-0.310315	1.1272251

The FARMAFIT subroutine estimates the parameters $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ , and $\text{[math]}$ of an ARFIMA( $\text{[math]}$ ) model. The log-likelihood function is solved by iterative numerical procedures such as the quasi-Newton optimization. The starting value $\text{[math]}$ is obtained by the approach of Geweke and Porter-Hudak (1983); the starting values of the AR and MA parameters are obtained from the least squares estimates.

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