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

series

specifies a time series with length.

d

specifies a fractional differencing order. This argument is required; the value of should be in the open interval excluding zero.

The FDIF subroutine returns the following value:

out

is an vector that contains the fractionally differenced process.

As an example, consider an ARFIMA() process

Let ; that is, follows an ARMA(1,1). The following statements compute the filtered series :

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;