cora {gogarch} | R Documentation |
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)
SSI |
Array with dimension dim = c(m, m, n) |
lag |
Integer, the lag for which the autocorrelation is computed. |
standardize |
Logical, if TRUE (the default), the
autocorrelation matrix is computed, otherwise the autocovariance
matrix. |
This function computes the autocorrelation matrix according to:
hat{Γ}_k (s) = frac{1}{n} sum_{t = k + 1}^n S_t S_{t-k}
hat{Phi}_k (s) = hat{Γ}_0 (s)^{-1/2} hat{Γ}_k (s) hat{Γ}_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{Γ}_0 (s)^{-1/2} is derived from the singular value decomposition of the co-variance matrix at lag zero.
cora |
Matrix with dimension dim = c(m, m) . |
Bernhard Pfaff
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.