Example 17.2: Cross-Spectral Analysis

The SPECTRA Procedure

Example 17.2: Cross-Spectral Analysis

This example shows cross-spectral analysis for two variables X and Y using simulated data. X is generated by an AR(1) process; Y is generated as white noise plus an input from X lagged 2 periods. All output options are specified on the PROC SPECTRA statement. PROC CONTENTS shows the contents of the OUT= data set.


   data a;
      xl = 0; xll = 0; 
      do i = - 10 to 100;
         x = .4 * xl  + rannor(123);
         y = .5 * xll + rannor(123);
         if i > 0 then output;
         xll = xl; xl = x; 
         end;
   run;
   
   proc spectra data=a out=b cross coef a k p ph s;
      var x y;
      weights 1 1.5 2 4 8 9 8 4 2 1.5 1;
   run;
   
   proc contents data=b position; 
   run;

The PROC CONTENTS report for the output data set B is shown in Output 17.2.1.

Output 17.2.1: Contents of PROC SPECTRA OUT= Data Set

The CONTENTS Procedure

Data Set Name:	WORK.B	Observations:	51
Member Type:	DATA	Variables:	17
Engine:	V8	Indexes:	0
Created:	12:39 Wednesday, April 28, 1999	Observation Length:	136
Last Modified:	12:39 Wednesday, April 28, 1999	Deleted Observations:	0
Protection:		Compressed:	NO
Data Set Type:	DATA	Sorted:	NO
Label:	Spectral Density Estimates

-----Variables Ordered by Position-----
#	Variable	Type	Len	Pos	Label
1	FREQ	Num	8	0	Frequency from 0 to PI
2	PERIOD	Num	8	8	Period
3	COS_01	Num	8	16	Cosine Transform of x
4	SIN_01	Num	8	24	Sine Transform of x
5	COS_02	Num	8	32	Cosine Transform of y
6	SIN_02	Num	8	40	Sine Transform of y
7	P_01	Num	8	48	Periodogram of x
8	P_02	Num	8	56	Periodogram of y
9	S_01	Num	8	64	Spectral Density of x
10	S_02	Num	8	72	Spectral Density of y
11	RP_01_02	Num	8	80	Real Periodogram of x by y
12	IP_01_02	Num	8	88	Imag Periodogram of x by y
13	CS_01_02	Num	8	96	Cospectra of x by y
14	QS_01_02	Num	8	104	Quadrature of x by y
15	K_01_02	Num	8	112	Coherency**2 of x by y
16	A_01_02	Num	8	120	Amplitude of x by y
17	PH_01_02	Num	8	128	Phase of x by y

The following statements plot the amplitude of the cross-spectrum estimate against frequency and against period for periods less than 25.


   symbol1 i=splines v=dot;
   proc gplot data=b;
      plot a_01_02 * freq;
   run;
   
   proc gplot data=b;
      plot a_01_02 * period;
      where period < 25;
   run;

The plot of the amplitude of the cross-spectrum estimate against frequency is shown in Output 17.2.2. The plot of the cross-spectrum amplitude against period for periods less than 25 observations is shown in Output 17.2.3.

Output 17.2.2: Plot of Cross-Spectrum Amplitude by Frequency

Output 17.2.3: Plot of Cross-Spectrum Amplitude by Period

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