TIMESERIES Procedure

Correlation Analysis

Correlation analysis can be performed on the working series by specifying the OUTCORR= option or one of the PLOTS= options that are associated with correlation. The CORR statement enables you to specify options that are related to correlation analysis.

Autocovariance Statistics

LAGS

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

N

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

ACOV

ModifyingAbove gamma With caret left-parenthesis h right-parenthesis equals StartFraction 1 Over upper T EndFraction sigma-summation Underscript t equals h plus 1 Overscript upper T Endscripts left-parenthesis y Subscript t Baseline minus y overbar right-parenthesis left-parenthesis y Subscript t minus h Baseline minus y overbar right-parenthesis

ACOV

ModifyingAbove gamma With caret left-parenthesis h right-parenthesis equals StartFraction 1 Over upper N Subscript h Baseline EndFraction sigma-summation Underscript t equals h plus 1 Overscript upper T Endscripts left-parenthesis y Subscript t Baseline minus y overbar right-parenthesis left-parenthesis y Subscript t minus h Baseline minus y overbar right-parenthesis when embedded missing values are present

Autocorrelation Statistics

ACF

ModifyingAbove rho With caret left-parenthesis h right-parenthesis equals ModifyingAbove gamma With caret left-parenthesis h right-parenthesis slash ModifyingAbove gamma With caret left-parenthesis 0 right-parenthesis

ACFSTD

normal upper S normal t normal d left-parenthesis ModifyingAbove rho With caret left-parenthesis h right-parenthesis right-parenthesis equals StartRoot StartFraction 1 Over upper T EndFraction left-parenthesis 1 plus 2 sigma-summation Underscript j equals 1 Overscript h minus 1 Endscripts ModifyingAbove rho With caret left-parenthesis j right-parenthesis squared right-parenthesis EndRoot

ACFNORM

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

ACFPROB

normal upper P normal r normal o normal b left-parenthesis ModifyingAbove rho With caret 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 left-parenthesis h right-parenthesis right-parenthesis EndAbsoluteValue right-parenthesis right-parenthesis

ACFLPROB

normal upper L normal o normal g normal upper P normal r normal o normal b left-parenthesis ModifyingAbove rho With caret 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 left-parenthesis h right-parenthesis right-parenthesis

ACF2STD

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

Partial Autocorrelation Statistics

PACF

ModifyingAbove phi With caret left-parenthesis h right-parenthesis equals normal upper Gamma Subscript left-parenthesis 0 comma h minus 1 right-parenthesis Baseline StartSet gamma Subscript j Baseline EndSet Subscript j equals 1 Superscript h

PACFSTD

normal upper S normal t normal d left-parenthesis ModifyingAbove phi With caret left-parenthesis h right-parenthesis right-parenthesis equals 1 slash StartRoot upper N 0 EndRoot

PCFNORM

normal upper N normal o normal r normal m left-parenthesis ModifyingAbove phi With caret left-parenthesis h right-parenthesis right-parenthesis equals ModifyingAbove phi With caret left-parenthesis h right-parenthesis slash normal upper S normal t normal d left-parenthesis ModifyingAbove phi With caret left-parenthesis h right-parenthesis right-parenthesis

PACFPROB

normal upper P normal r normal o normal b left-parenthesis ModifyingAbove phi With caret 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 phi With caret left-parenthesis h right-parenthesis right-parenthesis EndAbsoluteValue right-parenthesis right-parenthesis

PACFLPROB

normal upper L normal o normal g normal upper P normal r normal o normal b left-parenthesis ModifyingAbove phi With caret 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 phi With caret left-parenthesis h right-parenthesis right-parenthesis

PACF2STD

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

Inverse Autocorrelation Statistics

IACF

ModifyingAbove theta With caret left-parenthesis h right-parenthesis

IACFSTD

normal upper S normal t normal d left-parenthesis ModifyingAbove theta With caret left-parenthesis h right-parenthesis right-parenthesis equals 1 slash StartRoot upper N 0 EndRoot

IACFNORM

normal upper N normal o normal r normal m left-parenthesis ModifyingAbove theta With caret left-parenthesis h right-parenthesis right-parenthesis equals ModifyingAbove theta With caret left-parenthesis h right-parenthesis slash normal upper S normal t normal d left-parenthesis ModifyingAbove theta With caret left-parenthesis h right-parenthesis right-parenthesis

IACFPROB

normal upper P normal r normal o normal b left-parenthesis ModifyingAbove theta With caret 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 theta With caret left-parenthesis h right-parenthesis right-parenthesis EndAbsoluteValue right-parenthesis right-parenthesis

IACFLPROB

normal upper L normal o normal g normal upper P normal r normal o normal b left-parenthesis ModifyingAbove theta With caret 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 theta With caret left-parenthesis h right-parenthesis right-parenthesis

IACF2STD

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

White Noise Statistics

WN

upper Q left-parenthesis h right-parenthesis equals upper T left-parenthesis upper T plus 2 right-parenthesis sigma-summation Underscript j equals 1 Overscript h Endscripts rho left-parenthesis j right-parenthesis squared slash left-parenthesis upper T minus j right-parenthesis

WN

upper Q left-parenthesis h right-parenthesis equals sigma-summation Underscript j equals 1 Overscript h Endscripts upper N Subscript j Baseline rho left-parenthesis j right-parenthesis squared when embedded missing values are present

WNPROB

normal upper P normal r normal o normal b left-parenthesis upper Q left-parenthesis h right-parenthesis right-parenthesis equals chi Subscript max left-parenthesis 1 comma h minus p right-parenthesis Baseline left-parenthesis upper Q left-parenthesis h right-parenthesis right-parenthesis

WNLPROB

normal upper L normal o normal g normal upper P normal r normal o normal b left-parenthesis upper Q 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 upper Q left-parenthesis h right-parenthesis right-parenthesis

Last updated: June 19, 2025