The TIMESERIES Procedure

Cross-Correlation Analysis

Subsections:

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 variable y supplied in a CROSSVAR statement are:

LAGS

$h\in \{ 0, \ldots , H\} $

N

$N_ h$ is the number of observed products at lag h, ignoring missing values

CCOV

$\hat{\gamma }_{x,y}(h) = \frac{1}{T}\sum _{t=h+1}^{T} (x_ t - \overline{x}) (y_{t-h} - \overline{y})$

CCOV

$\hat{\gamma }_{x,y}(h) = \frac{1}{N_ h}\sum _{t=h+1}^{T} (x_ t - \overline{x}) (y_{t-h} - \overline{y})$ when embedded missing values are present

CCF

$\hat{\rho }_{x,y}(h)= \hat{\gamma }_{x,y}(h)/\sqrt {\hat{\gamma }_{x}(0)\hat{\gamma }_{y}(0)}$

CCFSTD

$Std(\hat{\rho }_{x,y}(h)) = 1/\sqrt {N_{0}}$

CCFNORM

$Norm(\hat{\rho }_{x,y}(h)) = \hat{\rho }_{x,y}(h)/Std(\hat{\rho }_{x,y}(h))$

CCFPROB

$Prob(\hat{\rho }_{x,y}(h)) = 2 \left( 1 - \Phi \left( |Norm(\hat{\rho }_{x,y}(h))| \right) \right)$

CCFLPROB

$LogProb(\hat{\rho }_{x,y}(h)) = -\log _{10} (Prob(\hat{\rho }_{x,y}(h))$

CCF2STD

$Flag(\hat{\rho }_{x,y}(h)) = \left\{ \begin{array}{l l} 1 & \hat{\rho }_{x,y}(h) > 2Std(\hat{\rho }_{x,y}(h)) \\ 0 & -2Std(\hat{\rho }_{x,y}(h))< \hat{\rho }_{x,y}(h) < 2Std(\hat{\rho }_{x,y}(h)) \\ -1 & \hat{\rho }_{x,y}(h) < -2Std(\hat{\rho }_{x,y}(h)) \\ \end{array} \right.$