The TIMESERIES Procedure

Correlation Analysis

Autocovariance Statistics
Autocorrelation Statistics
Partial Autocorrelation Statistics
Inverse Autocorrelation Statistics
White Noise Statistics

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: $h\in \{ 0, \ldots , H\}$
N: is the number of observed products at lag , ignoring missing values
ACOV: $\hat{\gamma }(h) = \frac{1}{T}\sum _{t=h+1}^{T} (y_ t - \overline{y}) (y_{t-h} - \overline{y})$
ACOV: $\hat{\gamma }(h) = \frac{1}{N_ h}\sum _{t=h+1}^{T} (y_ t - \overline{y}) (y_{t-h} - \overline{y})$ when embedded missing values are present

Autocorrelation Statistics

ACF: $\hat{\rho }(h)=\hat{\gamma }(h)/\hat{\gamma }(0)$
ACFSTD: $Std(\hat{\rho }(h)) = \sqrt {\frac{1}{T}\left( 1 + 2 \sum _{j=1}^{h-1}\hat{\rho }(j)^2 \right)}$
ACFNORM: $Norm(\hat{\rho }(h)) = \hat{\rho }(h)/Std(\hat{\rho }(h))$
ACFPROB: $Prob(\hat{\rho }(h)) = 2 \left( 1 - \Phi \left( |Norm(\hat{\rho }(h))| \right) \right)$
ACFLPROB: $LogProb(\hat{\rho }(h)) = -\log _{10} (Prob(\hat{\rho }(h))$
ACF2STD: $Flag(\hat{\rho }(h)) = \left\{ \begin{array}{l l} 1 & \hat{\rho }(h) > 2Std(\hat{\rho }(h)) \\ 0 & -2Std(\hat{\rho }(h))< \hat{\rho }(h) < 2Std(\hat{\rho }(h)) \\ -1 & \hat{\rho }(h) < -2Std(\hat{\rho }(h)) \\ \end{array} \right.$

Partial Autocorrelation Statistics

PACF: $\hat{\varphi }(h)=\Gamma _{(0, h-1)}\{ \gamma _ j\} ^ h_{j=1}$
PACFSTD: $Std(\hat{\varphi }(h)) = 1/\sqrt {N_0}$
PCFNORM: $Norm(\hat{\varphi }(h)) = \hat{\varphi }(h)/Std(\hat{\varphi }(h))$
PACFPROB: $Prob(\hat{\varphi }(h)) = 2 \left( 1 - \Phi \left( |Norm(\hat{\varphi }(h))| \right) \right)$
PACFLPROB: $LogProb(\hat{\varphi }(h)) = -\log _{10} (Prob(\hat{\varphi }(h))$
PACF2STD: $Flag(\hat{\varphi }(h)) = \left\{ \begin{array}{l l} 1 & \hat{\varphi }(h) > 2Std(\hat{\varphi }(h)) \\ 0 & -2Std(\hat{\varphi }(h))< \hat{\varphi }(h) < 2Std(\hat{\varphi }(h)) \\ -1 & \hat{\varphi }(h) < -2Std(\hat{\varphi }(h)) \\ \end{array} \right.$

Inverse Autocorrelation Statistics

IACF: $\hat{\theta }(h)$
IACFSTD: $Std(\hat{\theta }(h)) = 1/\sqrt {N_0}$
IACFNORM: $Norm(\hat{\theta }(h)) = \hat{\theta }(h)/Std(\hat{\theta }(h))$
IACFPROB: $Prob(\hat{\theta }(h)) = 2 \left( 1 - \Phi \left( |Norm(\hat{\theta }(h))| \right) \right)$
IACFLPROB: $LogProb(\hat{\theta }(h)) = -\log _{10} (Prob(\hat{\theta }(h))$
IACF2STD: $Flag(\hat{\theta }(h)) = \left\{ \begin{array}{l l} 1 & \hat{\theta }(h) > 2Std(\hat{\theta }(h)) \\ 0 & -2Std(\hat{\theta }(h))< \hat{\theta }(h) < 2Std(\hat{\theta }(h)) \\ -1 & \hat{\theta }(h) < -2Std(\hat{\theta }(h)) \\ \end{array} \right.$

White Noise Statistics

WN: $Q(h) = T(T+2)\sum _{j=1}^ h \rho (j)^2/ (T-j)$
WN: $Q(h) = \sum _{j=1}^ h N_ j \rho (j)^2$ when embedded missing values are present
WNPROB: $Prob(Q(h)) = \chi _{\max (1, h-p)} (Q(h))$
WNLPROB: $LogProb(Q(h)) = -\log _{10} (Prob(Q(h))$