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)
Matrix with dimension dim = c(m, m).
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.
Bernhard Pfaff
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.
gogarch