LiMcLeod {portes}

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),fitdf=0,sqrd.res=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", "arima0", "Arima", ("ARIMA forecast ARIMA Arima"), "lm", ("glm" "lm"), or "varest". obj may also an object with class "list" (see details and following examples).

lags

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

fitdf

Default is zero for testing the randomness of a given sequence with class "numeric", "matrix", "ts", or ("mts" "ts"). In general fitdf equals to the number of estimated parameters in the fitted model. If obj is an object with class "ar", "arima0", "Arima", "varest", ("ARIMA forecast ARIMA Arima"), or "list" then no need to enter the value of fitdf as it will be automatically determined. For obj with other classes, the fitdf is needed for degrees of freedom of asymptotic chi-square distribution.

sqrd.res

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

Details

However the portmanteau test statistic can be applied directly on the output objects from the built in R functions ar(), ar.ols(), ar.burg(), ar.yw(), ar.mle(), arima(), arim0(), Arima(), auto.arima(), lm(), glm(), and VAR(), it works with output objects from any fitted model. In this case, users should write their own function to fit any model they want, where they may use the built in R functions garch(), garchFit(), fracdiff(), tar(), etc. 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 fitdf of the fitted model (list(res = ..., fitdf = ...)). See the following example with the function FitModel().

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-fitdf) degrees of freedom.

Author(s)

Esam Mahdi and A.I. McLeod.

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

Box.test, BoxPierce, LjungBox, MahdiMcLeod, Hosking, portest, GetResiduals.

Examples

x <- rnorm(100)
LiMcLeod(x)                              ## univariate test
x <- cbind(rnorm(100),rnorm(100))
LiMcLeod(x)                              ## multivariate test 
##
##
## Monthly log stock returns of Intel corporation data: Test for ARCH Effects 
monthintel <- as.ts(monthintel)
LjungBox(monthintel)                         ## Usual test 
LjungBox(monthintel,sqrd.res=TRUE)  ## Test for ARCH effects 
##
##
## Quarterly, west German investment, income, and consumption from 1960 Q1 to 1982 Q4 
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 (fitdf will be automatically applied)
LiMcLeod(fit,lags,fitdf = 2)                          ## Correct (no need to specify fitdf)
LiMcLeod(fit,lags)                                    ## Correct
## Apply the test statistic on the residuals
res <- ts((fit$resid)[-(1:2), ])
LiMcLeod(res,lags,fitdf = 2)                          ## Correct
LiMcLeod(res,lags)                                    ## Wrong (fitdf is needed!)  
##
##
## Write a function to fit a model: Apply portmanteau test on fitted obj with class "list"
FitModel <- function(data){
    fit <- ar.ols(data, intercept = TRUE, order.max = 2)
    fitdf <- 2
    res <- res <- ts((fit$resid)[-(1:2), ]) 
 list(res=res,fitdf=fitdf)
}
data(WestGerman)
DiffData <- matrix(numeric(3 * 91), ncol = 3)
  for (i in 1:3) 
    DiffData[, i] <- diff(log(WestGerman[, i]), lag = 1)
Fit <- FitModel(DiffData)
LiMcLeod(Fit)