portes: ToeplitzBlock – R documentation

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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.

Author(s)

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).

Examples

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

portes

Portmanteau Tests for Univariate and Multivariate Time Series Models

v5.0

GPL (>= 2)

Authors

Esam Mahdi [aut, cre], Ian McLeod [ctb]

Initial release

2020-12-12