FDIF Call

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:

out

is an $n$ vector that contains the fractionally differenced process.

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 24.132: A Fractionally Differenced Process

zt
.
3.0146839
4.0190575
3.3402864
-0.41881
1.6149336
1.1998534
-0.137789
-1.475051
-1.670366