portes (version 6.0)

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 MahdiMcLeod.

Usage

ToeplitzBlock(res,Maxlag)

Value

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

Arguments

res

residuals, numeric or matrix.

Maxlag

an integer number = \(m\) is used to determined the order of the block matrix.

Author

Esam Mahdi and A.I. McLeod.

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, MahdiMcLeod, toeplitz

Examples

x <- rnorm(100)   
ToeplitzBlock(x,Maxlag=4)          ## Univariate Series
#
y <- cbind(rnorm(100),rnorm(100)) 
ToeplitzBlock(y,Maxlag=4)          ## Multivariate Series