Language Reference

CALL FDIF (out, series, d);

The FDIF subroutine computes a fractionally differenced process. The input arguments to the FDIF subroutine are as follows:

series: specifies a time series with n length.
d: specifies a fractional differencing order. This argument is required; the value of d should be in the open interval $(-1,1)$ excluding zero.

The FDIF subroutine returns the following value:

As an example, consider an ARFIMA( $1,0.3,1$ ) process

$(1-0.5B)(1-B)^{0.3}y_ t= (1+0.1B){\epsilon }_ t$

Let $z_ t=(1-B)^{0.3}y_ t$ ; that is, $z_ t$ follows an ARMA(1,1). The following statements compute the filtered series $z_ t$ :

d = 0.3;
phi = 0.5;
theta = -0.1;
call farmasim(yt, d, phi, theta) n=10 seed=1234;
call fdif(zt, yt, d);
print zt;

Figure 25.134: A Fractionally Differenced Process