portes (version 2-1)

LiMcLeod: The Modified Multivariate Portmanteau Test, Li-McLeod (1981)

Description

The modified multivariate portmanteau test suggested by Li and McLeod (1981).

Usage

LiMcLeod(obj,lags=seq(5,30,5),order=0,SquaredQ=FALSE)

Arguments

obj

a univariate or multivariate series with class "numeric", "matrix", "ts", or ("mts" "ts"). It can be also an object of fitted time-series model with class "ar",

lags

vector of lag auto-cross correlation coefficients used for LiMcLeod test.

order

needed for degrees of freedom of asymptotic chi-square distribution. If obj is an object with class "ar", "arima0", "Arima", "varest", "FitAR",

SquaredQ

if TRUE then apply the test on the squared values. This checks for Autoregressive Conditional Heteroscedastic, ARCH, effects. When SquaredQ = FALSE, then apply the test on

Value

• The multivariate test statistic suggested by Li and McLeod (1981) and its corresponding p-values for different lags based on the asymptotic chi-square distribution with k^2(lags-order) degrees of freedom.

Details

However the portmanteau test statistic can be applied directly on the output objects from the built in R functions ar(), FitAR(), arima(), arim0(), Arima(), auto.arima(), VAR(), garch(), garchFit(), FitFGN(), etc, it works with output objects from any fitted model. In this case, users should write their own function to fit any model they want. The object obj represents the output of this function. This output must be a list with at least two outcomes: the fitted residual and the order of the fitted model (list(res = ..., order = ...)). See the following example with the function FitModel().

References

Li, W. K. and McLeod, A. I. (1981). "Distribution of The Residual Autocorrelations in Multivariate ARMA Time Series Models". Journal of The Royal Statistical Society, Series B, 43, 231-239.

See Also

acf, Box.test, BoxPierce, LjungBox, Hosking, gvtest, portest, GetResiduals, tar

Examples

##############################################################
## Quarterly, west German investment, income, and consumption 
## from first quarter of 1960 to fourth quarter of 1982: 
##############################################################
data(WestGerman)
DiffData <- matrix(numeric(3 * 91), ncol = 3)
  for (i in 1:3) 
    DiffData[, i] <- diff(log(WestGerman[, i]), lag = 1)
fit <- ar.ols(DiffData, intercept = TRUE, order.max = 2)
lags <- c(5,10)
## Apply the test statistic on the fitted model 
LiMcLeod(fit,lags,order = 2)        ## Correct
LiMcLeod(fit,lags)                  ## Correct
## Apply the test statistic on the residuals
res <- ts((fit$resid)[-(1:2), ])
LiMcLeod(res,lags,order = 2)        ## Correct
LiMcLeod(res,lags)                  ## Wrong
##############################################################
## Write a function to fit a model 
## Apply portmanteau test on fitted obj with class "list"
##############################################################
## Example 1
FitModel <- function(data){
    fit <- ar.ols(data, intercept = TRUE, order.max = 2)
    order <- 2
    res <- res <- ts((fit$resid)[-(1:2), ]) 
 list(res=res,order=order)
}
Fit <- FitModel(DiffData)
LiMcLeod(Fit) 
##
## Example 2
library("TSA")
FitModel <- function(data){
    fit <- TSA::tar(y=log(data),p1=4,p2=4,d=3,a=0.1,b=0.9,print=FALSE)
    res <- ts(fit$std.res)
    p1 <- fit$p1
    p2 <- fit$p2
    order <- max(p1, p2)
    parSpec <- list(res=res,order=order)
  parSpec
}
data(prey.eq)
Fit <- FitModel(prey.eq)
LiMcLeod(Fit)