This function computes the autocorrelation matrix for a given lag. For instance, it is used for estimating GO-GARCH models whence the method of moments is utilized.
cora(SSI, lag = 1, standardize = TRUE)Array with dimension dim = c(m, m, n)
Integer, the lag for which the autocorrelation is computed.
Logical, if TRUE (the default), the
autocorrelation matrix is computed, otherwise the autocovariance
matrix.
Matrix with dimension dim = c(m, m).
This function computes the autocorrelation matrix according to:
$$ \hat{\Gamma}_k (s) = \frac{1}{n} \sum_{t = k + 1}^n S_t S_{t-k} $$ $$ \hat{\Phi}_k (s) = \hat{\Gamma}_0 (s)^{-1/2} \hat{\Gamma}_k (s) \hat{\Gamma}_0 (s)^{-1/2} $$
It is computationally assured that \(\hat{\Phi}_k (s)\) is symmetric by setting it equal to: \(\hat{\Phi}_k (s) = \frac{1}{2}(\hat{\Phi}_k (s) + \hat{\Phi}_k (s)')\). The standardization matrix \(\hat{\Gamma}_0 (s)^{-1/2}\) is derived from the singular value decomposition of the co-variance matrix at lag zero.
Boswijk, H. Peter and van der Weide, Roy (2009), Method of Moments Estimation of GO-GARCH Models, Working Paper, University of Amsterdam, Tinbergen Institute and World Bank.