To use the SPECTRA procedure, specify the input and output data sets and options for the analysis you want in the PROC SPECTRA statement, and list the variables to analyze in the VAR statement. The procedure produces no printed output unless the WHITETEST option is specified in the PROC SPECTRA statement. The periodogram, spectral density, and other results are written to the OUT= data set, depending on the options used.

For example, to compute the Fourier transform of a variable `X`

in a data set `A`

, use the following statements:

proc spectra data=a out=b coef; var x; run;

This PROC SPECTRA step writes the Fourier coefficients *a* and *b* to the variables `COS_01`

and `SIN_01`

in the output data set `B`

.

When a WEIGHTS statement is specified, the periodogram is smoothed by a weighted moving average to produce an estimate of
the spectral density of the series. The following statements write a spectral density estimate for `X`

to the variable `S_01`

in the output data set `B`

.

proc spectra data=a out=b s; var x; weights 1 2 3 4 3 2 1; run;

When the VAR statement specifies more than one variable, you can perform cross-spectral analysis by specifying the CROSS option
in the PROC SPECTRA statement. The CROSS option by itself produces the cross-periodograms for all two-way combinations of
the variables listed in the VAR statement. For example, the following statements write the real and imaginary parts of the
cross-periodogram of `X`

and `Y`

to the variables `RP_01_02`

and `IP_01_02`

in the output data set `B`

.

proc spectra data=a out=b cross; var x y; run;

To produce cross-spectral density estimates, specify both the CROSS option and the S option. The cross-periodogram is smoothed using the weights specified by the WEIGHTS statement in the same way as the spectral density. The squared coherency and phase estimates of the cross-spectrum are computed when the K and PH options are used.

The following example computes cross-spectral density estimates for the variables `X`

and `Y`

.

proc spectra data=a out=b cross s; var x y; weights 1 2 3 4 3 2 1; run;

The real part and imaginary part of the cross-spectral density estimates are written to the variables `CS_01_02`

and `QS_01_02`

, respectively.