The TIMESERIES Procedure

Cross-Correlation Analysis

Cross-Correlation Statistics

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 supplied in a VAR statement and variable supplied in a CROSSVAR statement are:

LAGS: $h\in \{ 0, \ldots , H\}$
N: is the number of observed products at lag , 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: $Flag(\hat{\rho }_{x,y}(h)) = \left\{ \begin{array}{l l} 1 & \hat{\rho }_{x,y}(h) > 2Std(\hat{\rho }_{x,y}(h)) \\ 0 & -2Std(\hat{\rho }_{x,y}(h))< \hat{\rho }_{x,y}(h) < 2Std(\hat{\rho }_{x,y}(h)) \\ -1 & \hat{\rho }_{x,y}(h) < -2Std(\hat{\rho }_{x,y}(h)) \\ \end{array} \right.$