FARMAFIT Call

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

The FARMAFIT subroutine estimates the parameters of an ARFIMA() 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.

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 value is 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.

0

requests the conditional sum of squares function. This is the default.

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() model:

     

In this model, . The following statements estimate the parameters of this model:

d = 0.3;
phi = 0.5;
theta = -0.1;
call farmasim(yt, d, phi, theta) seed=1234;
call farmafit(d, ar, ma, sigma, yt) p=1 q=1;
print d ar ma sigma;

Figure 23.110 Parameter Estimates for a ARFIMA Model
d ar ma sigma
0.3950157 0.5676217 -0.012339 1.2992989

The FARMAFIT subroutine estimates the parameters , , , and of an ARFIMA() model. The log-likelihood function is 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.