portes (version 5.0)

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,lag.max,season=1)

Arguments

res

residuals, numeric or matrix.

lag.max

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

season

seasonal periodicity given from MahdiMcLeod. Default is 1 for non seasonality cases.

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, MahdiMcLeod, toeplitz

Examples

# NOT RUN {
x <- rnorm(100)   
ToeplitzBlock(x,lag.max=4)          ## Univariate Series
#
y <- cbind(rnorm(100),rnorm(100)) 
ToeplitzBlock(y,lag.max=4)          ## Multivariate Series
#
ToeplitzBlock(y,lag.max=4,season=4) ## Multivariate Series
# }