portes (version 2.1-3)

ToeplitzBlock: Toeplitz Block Matrix of Hosking (1980) Auto and Cross Correlation Matrices

Description

Block Toeplitz matrix of order $m+1$ with $k\times k$ auto-cross correlation matrices. The Hosking (1980) definition of the correlation matrix is used. This is needed for the function gvtest.

Usage

ToeplitzBlock(res,lag.max,Kernel)

Arguments

res

residuals, numeric or matrix.

lag.max

an integer number = $m$ is used to determined the order of the block matrix.

Kernel

Logic number. default = FALSE. Parzen Kernel would be used for the autocorrelation function if setting TRUE

Value

A block Toeplitz matrix of auto and cross correlation matrices using Hosking (1980) definition from lag = $0$ to lag = $m$.

References

Hosking, J. R. M. (1980). "The Multivariate Portmanteau Statistic". Journal of American Statistical Association, 75, 602-608.

Lin, J.-W. and McLeod, A.I. (2006). "Improved Generalized Variance Portmanteau Test". Computational Statistics and Data Analysis, 51, 1731-1738.

Mahdi, E. and McLeod, A.I. (2011, accepted). "Improved Multivariate Portmanteau Test". Journal of Time Series Analysis. (JTSA - 3192).

See Also

acf, gvtest, toeplitz

Examples

## Univariate Series
x <- rnorm(100)
ToeplitzBlock(x,lag.max=4)
## Univariate Series with Parzen Kernel
x<-rnorm(100)
ToeplitzBlock(x,lag.max=4,Kernel=TRUE)

## Multivariate Series
x <- cbind(rnorm(100),rnorm(100))
ToeplitzBlock(x,lag.max=4)