The OUT= data set contains observations, if n is even, or observations, if n is odd, where n is the number of observations in the time series or the span of data being analyzed if missing values are present in the data. See the section Missing Values for details.
The variables in the new data set are named according to the following conventions. Each variable to be analyzed is associated with an index. The first variable listed in the VAR statement is indexed as 01, the second variable as 02, and so on. Output variables are named by combining indexes with prefixes. The prefix always identifies the nature of the new variable, and the indices identify the original variables from which the statistics were obtained.
Variables that contain spectral analysis results have names that consist of a prefix, an underscore, and the index of the
variable analyzed. For example, the variable S_01
contains spectral density estimates for the first variable in the VAR statement. Variables that contain crossspectral analysis
results have names that consist of a prefix, an underscore, the index of the first variable, another underscore, and the index
of the second variable. For example, the variable A_01_02
contains the amplitude of the crossspectral density estimate for the first and second variables in the VAR statement.
Table 26.3 shows the formulas and naming conventions used for the variables in the OUT= data set. Let X
be variable number nn in the VAR statement list and let Y
be variable number mm in the VAR statement list. Table 26.3 shows the output variables that contain the results of the spectral and crossspectral analysis of X
and Y
.
In Table 26.3 the following notation is used. Let be the vector of smoothing weights given by the WEIGHTS statement, normalized to sum to . Note that the weights are either explicitly provided using the constant specification or are implicitly determined by the kernel specification in the WEIGHTS statement.
The subscript of runs from to , so that is the middle weight in the list. Let , where .
Table 26.3: Variables Created by PROC SPECTRA
Variable 
Description 

FREQ 
frequency in radians from 0 to 
(Note: Cycles per observation is .) 

PERIOD 
period or wavelength: 
(Note: PERIOD is missing for FREQ=0.) 

COS_nn 

SIN_nn 
sine transform of X: 
P_nn 

S_nn 
spectral density estimate of X: 
RP_nn _mm 

IP_nn _mm 
imaginary part of crossperiodogram of X and Y: 


CS_nn _mm 
cospectrum estimate (real part of crossspectrum) of X and Y: 
QS_nn _mm 
quadrature spectrum estimate (imaginary part of crossspectrum) of X and Y: 
A_nn _mm 

K_nn _mm 

PH_nn _mm 
phase spectrum in radians of X and Y: 