portes (version 1.08)

LjungBox: 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),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 LjungBox test.

order

this is used for degrees of freedom of asymptotic chi-square distribution. If obj is a fitted time-series model with class "ar", "arima0", "Arima", "varest",

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 the usual resi

Value

• The Ljung and Box test statistic with the associated p-values for different lags based on the asymptotic chi-square distribution.

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

acf, Box.test, BoxPierce, Hosking, LiMcLeod, gvtest, portest, GetResiduals

Examples

x <- rnorm(100)
LjungBox(x)         
##############################################################
## Measurements of the annual flow of the river Nile at Aswan 
## from the years 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)               ## True 
LjungBox(fit, lags, order = 2)    ## True 
## Apply the test statistic on the residuals and set order = 2 
res <- resid(fit)
LjungBox(res, lags)               ## Not True  
LjungBox(res, lags, order = 2)    ## True 
##############################################################
## 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 
LjungBox(fit,lags)                ## True 
## Apply the test statistic on the residuals where order = 2
res <- ts((fit$resid)[-(1:2), ])
LjungBox(res,lags)                ## Not True 
LjungBox(res,lags,order = 2)      ## True 
##############################################################
## Monthly log stock returns of Intel corporation data
## Test for ARCH Effects 
##############################################################
monthintel <- as.ts(monthintel)
LjungBox(monthintel)                ## Usual test 
LjungBox(monthintel,SquaredQ=TRUE)  ## Test for ARCH effects