cora: Autocorrelations of a Matrix Process

In gogarch: Generalized Orthogonal GARCH (GO-GARCH) Models

Autocorrelations of a Matrix Process

Description

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.

Usage

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{Γ}_k (s) = \frac{1}{n} ∑_{t = k + 1}^n S_t S_{t-k}

\hat{Φ}_k (s) = \hat{Γ}_0 (s)^{-1/2} \hat{Γ}_k (s) \hat{Γ}_0 (s)^{-1/2}

It is computationally assured that \hat{Φ}_k (s) is symmetric by setting it equal to: \hat{Φ}_k (s) = \frac{1}{2}(\hat{Φ}_k (s) + \hat{Φ}_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.

Value

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

Author(s)

Bernhard Pfaff

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.

See Also

gogarch

gogarch documentation built on April 29, 2022, 5:06 p.m.