TIMESERIES Procedure

Cross-Correlation Analysis

Cross-correlation analysis can be performed on the working series by specifying the OUTCROSSCORR= option or one of the CROSSPLOTS= options that are associated with cross-correlation. The CROSSCORR statement enables you to specify options that are related to cross-correlation analysis.

Cross-Correlation Statistics

The cross-correlation statistics for the variable x supplied in a VAR statement and the variable y supplied in a CROSSVAR statement are as follows:

LAGS

h element-of StartSet negative upper H comma ellipsis comma 0 comma ellipsis comma upper H EndSet

N

upper N Subscript h is the number of observed products at lag h, ignoring missing values

CCOV

ModifyingAbove gamma With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction 1 Over upper M EndFraction sigma-summation Underscript t equals h plus 1 Overscript upper T Endscripts left-parenthesis x Subscript t Baseline minus x overbar right-parenthesis left-parenthesis y Subscript t minus h Baseline minus y overbar right-parenthesis 2nd Column 0 less-than-or-equal-to h less-than upper T 2nd Row 1st Column StartFraction 1 Over upper M EndFraction sigma-summation Underscript t equals StartAbsoluteValue h EndAbsoluteValue plus 1 Overscript upper T Endscripts left-parenthesis x Subscript t minus StartAbsoluteValue h EndAbsoluteValue Baseline minus x overbar right-parenthesis left-parenthesis y Subscript t Baseline minus y overbar right-parenthesis 2nd Column negative upper T less-than h less-than 0 EndLayoutwhere upper M equals upper N 0 if ADJSCALE=DEFAULT, upper M equals upper N Subscript h if ADJSCALE=UNBIASED, and upper M equals upper N 0 if ADJSCALE=BIASED

CCOV

ModifyingAbove gamma With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction 1 Over upper M EndFraction sigma-summation Underscript t equals h plus 1 Overscript upper T Endscripts left-parenthesis x Subscript t Baseline minus x overbar right-parenthesis left-parenthesis y Subscript t minus h Baseline minus y overbar right-parenthesis 2nd Column 0 less-than-or-equal-to h less-than upper T 2nd Row 1st Column StartFraction 1 Over upper M EndFraction sigma-summation Underscript t equals StartAbsoluteValue h EndAbsoluteValue plus 1 Overscript upper T Endscripts left-parenthesis x Subscript t minus StartAbsoluteValue h EndAbsoluteValue Baseline minus x overbar right-parenthesis left-parenthesis y Subscript t Baseline minus y overbar right-parenthesis 2nd Column negative upper T less-than h less-than 0 EndLayout when embedded missing values are present, where upper M equals upper N Subscript h if ADJSCALE=DEFAULT, upper M equals upper N Subscript h if ADJSCALE=UNBIASED, and upper M equals upper N 0 if ADJSCALE=BIASED

CCF

ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis equals ModifyingAbove gamma With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis slash StartRoot ModifyingAbove gamma With caret Subscript x Baseline left-parenthesis 0 right-parenthesis ModifyingAbove gamma With caret Subscript y Baseline left-parenthesis 0 right-parenthesis EndRoot

CCFSTD

normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis equals 1 slash StartRoot upper N 0 EndRoot

CCFNORM

normal upper N normal o normal r normal m left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis equals ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis slash normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis

CCFPROB

normal upper P normal r normal o normal b left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis equals 2 left-parenthesis 1 minus normal upper Phi left-parenthesis StartAbsoluteValue normal upper N normal o normal r normal m left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis EndAbsoluteValue right-parenthesis right-parenthesis

CCFLPROB

normal upper L normal o normal g normal upper P normal r normal o normal b left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis equals minus log Subscript 10 Baseline left-parenthesis normal upper P normal r normal o normal b left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis

CCF2STD

normal upper F normal l normal a normal g left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 2nd Column ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis greater-than 2 normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis 2nd Row 1st Column 0 2nd Column minus 2 normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis less-than ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis less-than 2 normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis 3rd Row 1st Column negative 1 2nd Column ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis less-than minus 2 normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret Subscript x comma y Baseline left-parenthesis h right-parenthesis right-parenthesis EndLayout

Last updated: June 19, 2025