PROC SIMILARITY: Sliding Similarity Analysis :: SAS/ETS(R) 9.22 User's Guide

The SIMILARITY Procedure

Example 23.3 Sliding Similarity Analysis

This example illustrates how to use sliding similarity analysis to compare two time sequences. The SASHELP.WORKERS data set contains two similar time series variables (ELECTRIC and MASONRY), which represent employment over time. The following statements create an example data set that contains two time series of differing lengths, where the variable MASONRY has the first 12 and last 7 observations set to missing to simulate the lack of data associated with the target series:

data workers; set sashelp.workers;
   if '01JAN1978'D <= date < '01JAN1982'D then masonry = masonry;
   else masonry = .;
run;

The goal of sliding similarity measures analysis is find the slide index that corresponds to the most similar subsequence of the input series when compared to the target sequence. The following statements perform sliding similarity analysis on the example data set:

proc similarity data=workers out=_NULL_ print=(slides summary);
   id date interval=month;
   input  electric;
   target masonry / slide=index measure=msqrdev
                    expand=(localabs=3 globalabs=3)
                    compress=(localabs=3 globalabs=3);
run;

The DATA=WORKERS option specifies that the input data set WORK.WORKERS is to be used in the analysis. The OUT=_NULL_ option specifies that no output time series data set is to be created. The PRINT=(SLIDES SUMMARY) option specifies that the ODS tables related to the sliding similarity measures and their summary be produced. The INPUT statement specifies that the input variable is ELECTRIC. The TARGET statement specifies that the target variable is MASONRY and that the similarity measure be computed using mean squared deviation (MEASURE=MSQRDEV). The SLIDE=INDEX option specifies observation index sliding. The COMPRESS=(LOCALABS=3 GLOBALABS=3) option limits local and global absolute compression to 3. The EXPAND=(LOCALABS=3 GLOBALABS=3) option limits local and global absolute expansion to 3.

Output 23.3.1 Summary of the Slide Measures

The SIMILARITY Procedure

Slide Measures Summary for Input=ELECTRIC and Target=MASONRY
Slide Index	DATE	Slide Target Sequence Length	Slide Input Sequence Length	Slide Warping Amount	Slide Minimum Measure
0	JAN1977	48	51	3	497.6737
1	FEB1977	48	51	1	482.6777
2	MAR1977	48	51	0	474.1251
3	APR1977	48	51	0	490.7792
4	MAY1977	48	51	-2	533.0788
5	JUN1977	48	51	-3	605.8198
6	JUL1977	48	51	-3	701.7138
7	AUG1977	48	51	3	646.5918
8	SEP1977	48	51	3	616.3258
9	OCT1977	48	51	3	510.9836
10	NOV1977	48	51	3	382.1434
11	DEC1977	48	51	3	340.4702
12	JAN1978	48	51	2	327.0572
13	FEB1978	48	51	1	322.5460
14	MAR1978	48	51	0	325.2689
15	APR1978	48	51	-1	351.4161
16	MAY1978	48	51	-2	398.0490
17	JUN1978	48	50	-3	471.6931
18	JUL1978	48	49	-3	590.8089
19	AUG1978	48	48	0	595.2538
20	SEP1978	48	47	-1	689.2233
21	OCT1978	48	46	-2	745.8891
22	NOV1978	48	45	-3	679.1907

Output 23.3.2 Minimum Measure

Minimum Measure Summary
Input Variable	MASONRY
ELECTRIC	322.5460

This analysis results in 23 slides based on the observation index. The minimum measure (322.5460) occurs at slide index 13 which corresponds to the time value FEB1978. Note that the original data set SASHELP.WORKERS was modified beginning at the time value JAN1978. This similarity analysis justifies the belief the ELECTRIC lags MASONRY by one month based on the time series cross-correlation analysis despite the lack of target data (MASONRY).

The goal of seasonal sliding similarity measures is to find the seasonal slide index that corresponds to the most similar seasonal subsequence of the input series when compared to the target sequence. The following statements repeat the preceding similarity analysis on the example data set with seasonal sliding:

proc similarity data=workers out=_NULL_ print=(slides summary);
   id date interval=month;
   input  electric;
   target masonry / slide=season measure=msqrdev;
run;

Output 23.3.3 Summary of the Seasonal Slide Measures

The SIMILARITY Procedure

Slide Measures Summary for Input=ELECTRIC and Target=MASONRY
Slide Index	DATE	Slide Target Sequence Length	Slide Input Sequence Length	Slide Warping Amount	Slide Minimum Measure
0	JAN1977	48	48	0	1040.086
12	JAN1978	48	48	0	641.927

Output 23.3.4 Seasonal Minimum Measure

Minimum Measure Summary
Input Variable	MASONRY
ELECTRIC	641.9273

The analysis differs from the previous analysis in that the slides are performed based on the seasonal index (SLIDE=SEASON) with no warping. With a seasonality of 12, two seasonal slides are considered at slide indices 0 and 12 with the minimum measure (641.9273) occurring at slide index 12 which corresponds to the time value JAN1978. Note that the original data set SASHELP.WORKERS was modified beginning at the time value JAN1978. This similarity analysis justifies the belief that ELECTRIC and MASONRY have similar seasonal properties based on seasonal decomposition analysis despite the lack of target data (MASONRY).

Note: This procedure is experimental.

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