cora() R function from [gogarch]

Autocorrelations of a Matrix Process

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. latin1


cora(SSI, lag = 1, standardize = TRUE)

Arguments

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.

Details

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: c(" $\\hat{\\Phi}_k (s) = \\frac{1}{2}(\\hat{\\Phi}_k (s) +\n$ ", " $\\hat{\\Phi}_k (s)')$ "). The standardization matrix c(" $\\hat{\\Gamma}_0\n$ ", " $(s)^{-1/2}$ ") is derived from the singular value decomposition of the co-variance matrix at lag zero.

Returns

cora: Matrix with dimension dim = c(m, m).

References

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.

Author(s)

Bernhard Pfaff

cora function