portes (version 2-1)

BoxPierce: The Univariate-Multivariate Box and Pierce Portmanteau Test

Description

The univariate or multivariate Box-Pierce (1970) portmanteau test.

Usage

BoxPierce(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 BoxPierce 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 Box and Pierce univariate or multivariate test statistic with the associated 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

Box, G.E.P. and Pierce, D.A. (1970). "Distribution of Residual Autocorrelation in Autoregressive-Integrated Moving Average Time Series Models". Journal of American Statistical Association, 65, 1509-1526.

See Also

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

Examples

x <- rnorm(100)
BoxPierce(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 
BoxPierce(fit, lags)               ## Correct 
BoxPierce(fit, lags, order = 2)    ## Correct 
## Apply the test statistic on the residuals and set order = 2 
res <- resid(fit)
BoxPierce(res, lags)               ## Wrong  
BoxPierce(res, lags, order = 2)    ## Correct 
##############################################################
## 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 
BoxPierce(fit,lags)                ## Correct 
## Apply the test statistic on the residuals where order = 2
res <- ts((fit$resid)[-(1:2), ])
BoxPierce(res,lags)                ## Wrong 
BoxPierce(res,lags,order = 2)      ## Correct 
##############################################################
## Monthly log stock returns of Intel corporation data
## Test for ARCH Effects 
##############################################################
monthintel <- as.ts(monthintel)
BoxPierce(monthintel)                ## Usual test 
BoxPierce(monthintel,SquaredQ=TRUE)  ## Test for ARCH effects
##############################################################
## Write a function to fit a model 
## Apply portmanteau test on fitted obj with class "list"
##############################################################
## Example 1
library("FitAR")
FitModel <- function(data){
    fit <- FitAR(z=data,p=2)
    p <- length(fit$phiHat)
    order <- p
    res <- fit$res 
 list(res=res,order=order)
}
Fit <- FitModel(Nile)
BoxPierce(Fit) 
##
## Example 2
library("TSA")
FitModel <- function(data){
    fit <- TSA::tar(y=log(data),p1=4,p2=4,d=3,a=0.1,b=0.9,print=FALSE)
    res <- ts(fit$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)
BoxPierce(Fit)