FARMAFIT Call
estimate the parameters of an ARFIMA() model
- CALL FARMAFIT( d, phi, theta, sigma, series
<, p, q, opt>);
The inputs 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=0.
If you specify p=3,
the FARMAFIT subroutine estimates the coefficient of the
lagged variable .
If you specify p=,
the FARMAFIT subroutine estimates the coefficients of
lagged variables , , and .
- q
- specifies the subset of the MA order.
If you do not specify q, the default is q=0.
If you specify q=2,
the FARMAFIT subroutine estimates the coefficient of the
lagged variable .
If you specify q=,
the FARMAFIT subroutine estimates the coefficients of
lagged variables and .
- 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 containing a fractional differencing order.
- phi
- is a vector containing the autoregressive coefficients.
- theta
- is a vector containing the moving-average coefficients.
- sigma
- is a scalar containing a variance of the innovation series.
Consider the following ARFIMA(
) model:
In this model,
.
To estimate the parameters of this model, you can use the following code:
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;
The FARMAFIT subroutine estimates parameters ,
, , and
of an ARFIMA() model.
The log-likelihood function needs to be solved by iterative
numerical procedures such as the quasi-Newton optimization.
The starting value 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.
Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.