Different Correlations from PROC TIMESERIES and PROC CORR

[hussier1]

I ran a cross-correlation analysis using PROC TIMESERIES, and found a correlation of 0.51695 at a lag of 1. I wanted to then find the associated significance level, so I created a new data set with the appropriate lag and applied PROC CORR, which gave me 0.52006. I also tested the correlation w/o any lag and both gave me exactly 0.1460650864, so I presume it's an error somewhere with the lagging. I looked at the outputted datasets however, and it all seems to be in order. The difference is pretty minor, but should I be concerned?

proc timeseries data=final2 crossplots=ccf outcrosscorr=final3;
id weeks interval=day accumulate=none;
var ncresiduals gtresiduals;
run;


data final4;
set final2;
gt3=lag(gtresiduals);
run;

proc corr pearson data=final4 out=final5;
var gt3;
with ncresiduals;
run;

[PaigeMiller]

PROC TIMESERIES (as far as I know), does not compute correlations, it computes auto-correlations, and so this should not be the same as PROC CORR which does computer correlations.

[hussier1]

I based my code on this : https://support.sas.com/documentation/cdl/en/etsug/63939/HTML/default/viewer.htm#etsug_timeseries_se..., and the graphical output is marked "cross-correlation" on top, so I don't think that's the issue.

[PaigeMiller]

Cross correlations from PROC TIMESERIES are not the same as CORRELATIONS from PROC CORR. I don't think they should match.

[hussier1]

If they're done at the same lag, shouldn't they? They match for lag zero, and did match when I did something similar with a different dataset.

[MichaelL_SAS · Accepted solution]

The formulas on the documentation page you provided explain why you are not getting the same values when there is a lag. Note that in the cross covariance formula it is always the mean of y that is being used regardless of the lag value. In your example code the variables gtresiduals (y) and gt3 (the lagged values you created) will (very likely) have different means. As @PaigeMiller said the two procedures are computing different quantities.