portest: Portmanteau Test Statistics

Description

Univariate or multivariate portmanteau test statistics based on the Monte-Carlo techniques or asymptotic distributions.

Usage

portest(obj,lags=seq(5,30,5),order=0,test=c("gvtest","BoxPierce",
    "LjungBox","Hosking","LiMcLeod"),MonteCarlo=TRUE,nslaves=1,
     NREP=1000,InfiniteVarianceQ=FALSE,SquaredQ=FALSE,
     func=list(SimModel=NULL,FitModel=NULL),pkg=NULL,SetSeed=TRUE)

Arguments

obj

if obj is an object of class "ar", "arima0", "Arima", "varest", "FitAR", "FitFGN", "garch", "fGARCH", or "list"

lags

vector of lag values is used for portmanteau test.

order

as described in BoxPierce, gvtest, Hosking, LiMcLeod, and LjungBox and needed only when MonteCarlo = FALSE is selected.

test

portmanteau test statistic type

MonteCarlo

if TRUE then apply the Monte-Carlo version of portmanteau statistic. Otherwise, apply the asymptotic distribution.

nslaves

number of slaves needed to use in parallel calculations. Default is one single CPU.

NREP

number of replications needed for Monte-Carlo test.

InfiniteVarianceQ

FALSE, assumes innovations with finite variance. Otherwise, innovations follow stable distribution with infinite variance.

SquaredQ

as described in BoxPierce, gvtest, Hosking, LiMcLeod, and LjungBox.

func

additional argument defined as a list with two specified functions, SimModel and FitModel. This argument is needed when the class of obj is "list" (see details

pkg

the name of the library to be loaded if the Monte-Carlo significance test is used with an object obj with class "list".

SetSeed

if TRUE then set.seed is initialized.

Value

The portmanteau test statistic with the associated p-values for different lag values.

Details

The portmanteau test statistics, gvtest, BoxPierce, LjungBox, Hosking, and LiMcLeod are implemented based on the Monte-Carlo techniques and the approximation asymptotic distributions as described in Mahdi and McLeod (2012). The null hypothesis assuming that the fitted model is an adequate model and the residuals behave like white noise series. The parallel computing program MPICH2 must be properly installed in the I O environment system in which the portes package will run if one decide to choose the argument MonteCarlo=TRUE provided that nslaves equals to a positive integer more than 1. This function can be used for testing the adequacy in the nonseasonal fitted ARIMA, VAR, and Fractional Gaussian Noise, FGN, models. Also, it can be used to check for randomness as well as for GARCH effects. Any other fitted model, for example, threashold autoregression model, may also be tested for adequacy. In this case, two functions, SimModel() and FitModel(), must be provided via the argument func. The object obj is the output of the fitted model coded in the function FitModel and it is a "list" with at least res, the residuals from the fitted model in FitModel(). The output from the function SimModel() is a simulated univariate or multivariate series from the fitted model coded in the function FitModel(). The argument pkg represents the name of the R package where the fitted model build in (see the last two examples).

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. Hosking, J. R. M. (1980). "The Multivariate Portmanteau Statistic". Journal of American Statistical Association, 75, 602-608. Li, W. K. and McLeod, A. I. (1981). "Distribution of The Residual Autocorrelations in Multivariate ARMA Time Series Models". Journal of The Royal Statistical Society, Series B, 43, 231-239. Lin, J.-W. and McLeod, A.I. (2006). "Improved Generalized Variance Portmanteau Test". Computational Statistics and Data Analysis 51, 1731-1738. Lin, J.-W. and McLeod, A.I. (2008). "Portmanteau Tests for ARMA Models with Infinite Variance". Journal of Time Series Analysis, 29, 600-617. Ljung, G.M. and Box, G.E.P (1978). "On a Measure of Lack of Fit in Time Series Models". Biometrika, 65, 297-303. Mahdi, E. and McLeod, A.I. (2012). "Improved Multivariate Portmanteau Test". Journal of Time Series Analysis, 33(2), 211-222. McLeod A.I, Li W.K (1983). "Distribution of the Residual Autocorrelation in Multivariate ARMA Time Series Models". Journal of Time Series Analysis, 4, 269-273. 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. Tierney, L., Rossini, A. J., Li, N., and Sevcikova, H. (2009). snow: Simple Network of Workstations. R package version 0.3-10. http://CRAN.R-project.org/package=snow. Wuertz, D. and core team members R (2012). fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling. R package version 2150.81. http://CRAN.R-project.org/package=fGarch. Yu, H. (2002). Rmpi: Parallel Statistical Computing in R. R News, 2(2), 10-14. http://CRAN.R-project.org/doc/Rnews.

Examples

Run this code

#to save time the other examples are not run
#########################################################################
####                                                                 ####
####                   Monte-Carlo Portmanteau Tests                 ####  
####                                                                 #### 
#########################################################################
## Monte-Carlo test for randomness series                              ##
#########################################################################
data("DEXCAUS")
returns <- log(DEXCAUS[-1]/DEXCAUS[-length(DEXCAUS)])
portest(returns)            ## MC using one CPU takes about 25.16 seconds
portest(returns, nslaves=4) ## MC using 4 CPUs takes about 9.51 seconds
portest(returns, MonteCarlo=FALSE)                 ## asymptotic gvtest
portest(returns,test="LjungBox", MonteCarlo=FALSE) ## asymptotic LjungBox 
#########################################################################
## Monte-Carlo goodness-of-fit arima test using 4 CPUs                 ##
#########################################################################
## arima() or Arima() function takes about 14.32 seconds
ans1 <- arima(WWWusage,order=c(3,1,0))
portest(ans1, nslaves = 4)
#
## arima0() function takes about 15.26 seconds
ans2 <- arima0(WWWusage,order=c(3,1,0))
portest(ans2, nslaves = 4)
#
## auto.arima() function from package forecast takes about 13.59 seconds
library("forecast")
ans3 <- auto.arima(WWWusage)
portest(ans3, nslaves = 4)
#
## ar() function takes about 9.39 seconds
ans4 <- ar(Nile,order.max=2)
portest(ans4, nslaves = 4)
#
## FitAR() function takes about 10.78 seconds
library("FitAR")
ans5 <- FitAR(Nile, p=2)
portest(ans5, nslaves = 4)
#########################################################################
## Monte-Carlo goodness-of-fit VAR test - Multivariate series     ##
#########################################################################
data("IbmSp500")
ibm <- log(IbmSp500[,2]+1)*100
sp500 <- log(IbmSp500[,3]+1)*100
IBMSP500 <- data.frame(cbind(ibm,sp500))
## ar.ols() function takes about 9.11 seconds
ans6 <-  ar.ols(IBMSP500, aic=FALSE, intercept=TRUE, order.max=5)
portest(ans6, NREP=100, test="gvtest", nslaves=4)
## VAR() function takes about 11.55 seconds
library("vars")
ans7 <- VAR(IBMSP500, p=5) 
portest(ans7, NREP=100, test="gvtest", nslaves=4)
portest(ans7,test="Hosking", MonteCarlo=FALSE) ## asymptotic Hosking test
#########################################################################
## Monte-Carlo test for GARCH effects using 4 CPUs                     ##
#########################################################################
## Example 1
## Test for ARCH effects on returns series takes about 14.65 seconds
data("monthintel")
returns <- as.ts(monthintel)
lags <- c(5, 10, 20, 40)
portest(returns, lags = lags, nslaves = 4, SquaredQ = TRUE)
#
## Example 2
library("fGarch")
library("tseries")
data("GNPDEF")
z<-ts(GNPDEF[,2], start=1947, freq=4)
r <- 100*diff(log(z))
## use garch() function takes about 6.75 seconds
FitGarch1 <- garch(r, order = c(1,1))
portest(FitGarch1,NREP=100,nslaves = 4)
portest(FitGarch1,NREP=100,nslaves = 4,SquaredQ=TRUE)
#
## use garchFit() function takes about 13.56 seconds
GarchFit2 <- garchFit(formula = ~arma(4,0)+garch(1,1), data=r, trace=FALSE)
portest(GarchFit2, NREP=100, nslaves = 4, SquaredQ = FALSE)
portest(GarchFit2, NREP=100, nslaves = 4, SquaredQ = TRUE)
#########################################################################
## Monte-Carlo test on residuals with infinite variances               ##
#########################################################################
## It takes about 32.7 seconds on personal PC with 4 CPUs 
data("CRSP")
CRSP.AR5<- arima(CRSP, c(5, 0, 0))
lags <- c(10, 20, 30)
portest(CRSP.AR5,lags=lags,nslaves=4,NREP=1000,InfiniteVarianceQ=TRUE)      
#########################################################################
## Monte-Carlo test for Fractional Gaussian Noise, FGN.                ##
#########################################################################
## It takes about 55.06 seconds on personal PC with 4 CPUs 
library("FGN")
data("NileMin")
NILE.FGN <- FitFGN(NileMin)
lags <- c(5, 10, 20)
portest(NILE.FGN, lags = lags, nslaves = 4) 
portest(NILE.FGN, MonteCarlo=FALSE)  ## asymptotic distribution method
##############################################################
## Write two functions to fit a model and simulate results 
## Apply Monte-Carlo test on fitted obj with class "list"
##############################################################
## Example 1 
## Threshold Autoregressive (TAR) Model example from TSA package
## It takes about 64.27 seconds on personal PC with 4 CPUs
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$std.res)
    parSpec <- list(res=res,fit=fit)
  parSpec
}
SimModel <- function(parSpec){
    fit <- parSpec$fit   
  exp(tar.sim(fit)$y)
}
data(prey.eq)
portest(FitModel(prey.eq),nslaves=4,func=list(SimModel,FitModel),pkg="TSA")
#
## Example 2
## It takes about 10.75 seconds on personal PC with 4 CPUs
FitModel <- function(data){
    fit <- ar(data,aic = FALSE, order.max=2)
    order <- 2
    res <- ts(fit$resid[-(1:order)]) 
    phi <- fit$ar
    theta <- NULL
    sigma <- fit$var.pred
    demean <- fit$x.mean
 list(res=res,phi=phi,theta=theta,sigma=sigma,demean=demean)
}
SimModel <- function(parSpec){
    res <- parSpec$res
    n <- length(res)  
    innov <- sample(x=res,size=n,replace = TRUE)  
    phi <- parSpec$phi
    theta <- parSpec$theta
    sigma <- parSpec$sigma 
    demean <- parSpec$demean 
   arima.sim(n = n, list(ar = phi, ma = theta), innov = innov, 
             sd = sqrt(sigma), mean = demean)
}
Fit <- FitModel(Nile)
portest(Fit,nslaves=4,func=list(SimModel=SimModel,FitModel=FitModel),pkg="stats")

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