portes (version 2-1)

gvtest: Generalized Variance Portmanteau Test

Description

New generalized variance portmanteau test based on the determinant of the Hosking's autocorrelation block Toeplitz matrix with order $m+1$ given in the function ToeplitzBlock, where $m$ represents the order of the block matrix.

Usage

gvtest(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 gvtest 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 generalized variance portmanteau test statistic and its associated p-values for different lags based on asymptotic chi-square as given in Mahdi and McLeod (2012).

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

Mahdi, E. and McLeod, A.I. (2012). "Improved Multivariate Portmanteau Test". Journal of Time Series Analysis, 33(2), 211-222. Pena, D. and Rodriguez, J. (2002). "A Powerful Portmanteau Test of Lack of Test for Time Series". Journal of American Statistical Association, 97, 601-610. Pena, D. and Rodriguez, J. (2006). "The log of the determinant of the autocorrelation matrix for testing goodness of fit in time series". Journal of Statistical Planning and Inference, 136, 2706-2718.

See Also

acf, Box.test, BoxPierce, LjungBox, Hosking, LiMcLeod, portest, ToeplitzBlock, GetResiduals, tar

Examples

x <- rnorm(100)
gvtest(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, 30)
## Apply the univariate test statistic on the fitted model 
gvtest(fit, lags)               ## Correct 
gvtest(fit, lags, order = 2)    ## Correct 
## Apply the test statistic on the residuals and set order = 2 
res <- resid(fit)
gvtest(res, lags)               ## Wrong  
gvtest(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 <- seq(5,30,5)
## Apply the test statistic on the fitted model 
gvtest(fit,lags)                ## Correct 
## Apply the test statistic on the residuals where order = 2
res <- ts((fit$resid)[-(1:2), ])
gvtest(res,lags)                ## Wrong 
gvtest(res,lags,order = 2)      ## Correct 
##############################################################
## Monthly log stock returns of Intel corporation data
## Test for ARCH Effects 
##############################################################
monthintel <- as.ts(monthintel)
gvtest(monthintel)                ## Usual test
gvtest(monthintel,SquaredQ=TRUE)  ## Test for ARCH effects
##############################################################
## Write a function to fit a model 
## Apply portmanteau test on fitted obj with class "list"
##############################################################
## Example 1
library("FitAR")
FitModel <- function(data){
    fit <- FitAR(z=data,p=2)
    p <- length(fit$phiHat)
    order <- p
    res <- fit$res 
 list(res=res,order=order)
}
Fit <- FitModel(Nile)
gvtest(Fit) 
##
## Example 2
library("TSA")
FitModel <- function(data){
    fit <- TSA::tar(y=log(data),p1=4,p2=4,d=3,a=0.1,b=0.9,print=FALSE)
    res <- ts(fit$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)
gvtest(Fit)