A SPECTRA statement can be used with the TIMESERIES procedure to specify which statistics appear in the OUTSPECTRA= data set. The SPECTRA statement options are used in performing a spectral analysis on the variables listed in the VAR statement. These options affect values that are produced in the PROC TIMESERIES statement’s OUTSPECTRA= data set, and in the periodogram and spectral density estimate. Only one SPECTRA statement is allowed.
The following univariate frequency domain statistics are available:
frequency in radians from 0 to
period or wavelength
cosine transform
sine transform
periodogram
spectral density estimates
If none of the frequency domain statistics are specified, the default is as follows:
spectra period p;
The following options can be specified in the SPECTRA statement following the slash (/):
You can further parameterize each of the kernel functions with a kernel scale factor by using the C= and E= options. The default values of the kernel scale parameters, c and e, that are associated with each of the kernel functions together with their kernel scale factor values, M, for a series with 100 periodogram ordinates are listed in Table 32.2. The formula that is used to generate the table entries is , where K is the number of Fourier component frequencies.
Table 32.2: Default Kernel Scale Factor Parameters
Kernel |
c |
e |
M |
Bartlett |
1/2 |
1/3 |
2.32 |
Parzen |
1 |
1/5 |
2.51 |
Quadratic |
1/2 |
1/5 |
1.26 |
Tukey-Hanning |
2/3 |
1/5 |
1.67 |
Truncated |
1/4 |
1/5 |
0.63 |
For example, to apply the truncated kernel by using default scale factor parameters in the frequency domain, you could use the following SPECTRA statement:
spectra / truncat;
For more information about the kernel function parameterization and the DOMAIN= option, see the section Using Kernel Specifications.