portes (version 2.1-3)

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", "arima0", "Arima", "varest", "FitAR", "FitFGN", "garch", or "fGARCH". obj may also an object with class "list" (see details and following example).

lags

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

order

needed for degrees of freedom of asymptotic chi-square distribution. If obj is an object with class "ar", "arima0", "Arima", "varest", "FitAR", "FitFGN", "garch", "fGARCH", or "list" then no need to enter the value of order as it will be automatically determined. In general order equals to the number of estimated parameters in the fitted model.

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 residuals.

Value

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

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, tar

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)               ## Correct 
LjungBox(fit, lags, order = 2)    ## Correct 
## Apply the test statistic on the residuals and set order = 2 
res <- resid(fit)
LjungBox(res, lags)               ## Wrong  
LjungBox(res, lags, order = 2)    ## Correct 
#to save time the other examples are not run
## Not run: 
# ##############################################################
# ## 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)                ## Correct 
# ## Apply the test statistic on the residuals where order = 2
# res <- ts((fit$resid)[-(1:2), ])
# LjungBox(res,lags)                ## Wrong 
# LjungBox(res,lags,order = 2)      ## Correct 
# ##############################################################
# ## Monthly log stock returns of Intel corporation data
# ## Test for ARCH Effects 
# ##############################################################
# monthintel <- as.ts(monthintel)
# LjungBox(monthintel)                ## Usual test 
# LjungBox(monthintel,SquaredQ=TRUE)  ## Test for ARCH effects
# ##############################################################
# ## Write a function to fit a model 
# ## Apply portmanteau test on fitted obj with class "list"
# ##############################################################
# ## Example 1
# library("FitAR")
# FitModel <- function(data){
#     fit <- FitAR(z=data,p=2)
#     p <- length(fit$phiHat)
#     order <- p
#     res <- fit$res 
#  list(res=res,order=order)
# }
# Fit <- FitModel(Nile)
# LjungBox(Fit)
# ##
# ## Example 2
# library("TSA")
# FitModel <- function(data){
#     fit <- TSA::tar(y=log(data),p1=4,p2=4,d=3,a=0.1,b=0.9,print=FALSE)
#     res <- ts(fit$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) 
# LjungBox(Fit)
# ## End(Not run)