LjungBox {portes}

Ljung and Box Portmanteau Test

Description

The Ljung-Box (1978) modified portmanteau test. In the multivariate time series, this test statistic is asymptotically equal to Hosking.

Usage

LjungBox(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().

Note: In stats R, the function Box.test was built to compute the Box and Pierce (1970) and Ljung and Box (1978) test statistics only in the univariate case where we can not use more than one single lag value at a time. The functions BoxPierce and LjungBox are more accurate than Box.test function and can be used in the univariate or multivariate time series at vector of different lag values as well as they can be applied on an output object from a fitted model described in the description of the function BoxPierce.

Value

The Ljung and Box test statistic with the associated 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

Ljung, G.M. and Box, G.E.P (1978). "On a Measure of Lack of Fit in Time Series Models". Biometrika, 65, 297-303.

See Also

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

Examples

x <- rnorm(100)
LjungBox(x)                              ## univariate test
x <- cbind(rnorm(100),rnorm(100))
LjungBox(x)                              ## multivariate test      
##
##
## Annual flow of the river Nile at Aswan - 1871 to 1970
fit <- arima(Nile, c(1, 0, 1))
lags <- c(5, 10, 20)
## Apply the univariate test statistic on the fitted model 
LjungBox(fit, lags)            ## Correct (no need to specify fitdf) 
LjungBox(fit, lags, fitdf = 2) ## Correct 
## Apply the test statistic on the residuals and set fitdf = 2 
res <- resid(fit)
LjungBox(res, lags)             ## Wrong (fitdf is needed!)  
LjungBox(res, lags, fitdf = 2)  ## Correct 
##
##
## 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 
LjungBox(fit,lags)                ## Correct (no need to specify fitdf)
## Apply the test statistic on the residuals where fitdf = 2
res <- ts((fit$resid)[-(1:2), ])
LjungBox(res,lags)                ## Wrong (fitdf is needed!)  
LjungBox(res,lags,fitdf = 2)      ## Correct 
##
##
## Monthly log stock returns of Intel corporation data: Test for ARCH Effects 
monthintel <- as.ts(monthintel)
LjungBox(monthintel)                         ## Usual test 
LjungBox(monthintel,sqrd.res=TRUE)  ## Test for ARCH effects
##
#### Write a function to fit a model: Apply portmanteau test on fitted obj with class "list"
## Example
FitModel <- function(data){
    fit <- ar.ols(data, intercept = TRUE, order.max = 2)
    fitdf <- 2
    res <- res <- ts((fit$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)
LjungBox(Fit)