portes (version 1.04)

portes: Parametric Bootstrap Portmanteau Tests

Description

Univariate or multivariate GVStat and LiMcLeod portmanteau tests using parametric bootstrap techniques.

Usage

portes(obj, lags=seq(5,30,5), statistic=c("GVStat","LiMcLeod"), 
  order=0, SpawnSlaves=c("default","Rmpi","snow"), nslaves=2, 
  NREP=1000, InfiniteVarianceQ=FALSE,SquaredQ=FALSE, Set.Seed=TRUE)

Arguments

obj

if obj is an object of class "ar", "Arima", "arima0", "FitAR", or "FitFGN" then a portmanteau goodness-of-fit test is done on the fitted model. Otherwise, for

lags

vector of lag values is used for portmanteau test.

statistic

character string giving the name of the portmanteau test, default is "GVStat".

order

$p+q$, where ($p$,$q$) is the ARMA or the VARMA order.

SpawnSlaves

"default" when a computer with single CPU is used, "Rmpi" or "snow" when a computer with MultiCore CPUs is used.

nslaves

number of slaves needed to use in parallel calculations.

NREP

number of replications needed for parametric bootstrap test.

InfiniteVarianceQ

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

SquaredQ

TRUE, apply the test to the squared values. This is needed to check the Autoregressive Conditional Heteroscedastic, ARCH, effects. When SquaredQ = FALSE, apply for the usual residuals.

Set.Seed

initialize random seed.

Value

• vector of p-values for different lag values.

Details

The generalized variance portmanteau statistic, GVStat, and the modified portmanteau statistic, LiMcLeod, are implemented based on parametric bootstrap techniques. The null hypothesis assuming that the fitted model is an adequate model and the residuals behave like white noise series. The Rmpi package must be installed if one decide to choose the argument SpawnSlaves="Rmpi" and the snow package must be installed if one decide to choose the argument SpawnSlaves="snow". This function can be used for testing ARCH effects, and for checking adequacy in the fitted ARMA, VAR, and Fractional Gaussian Noise, FGN, models. Also, it can be used to check for randomness of residuals.

References

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. Mahdi, E. and McLeod, A.I. (2010). "Improved Multivariate Portmanteau Diagnostic Test". Submitted. McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007). "Algorithms for Linear Time Series Analysis". Journal of Statistical Software.

See Also

simvarma, ar, arima, arima0, FitAR, FitFGN, LiMcLeod, GVStat, FitStable

Examples

#Example 1
#Simple example using portes.
# 100 replications takes about 6 seconds on single cpu 2.67 GHz
ans<-arima(Nile, order=c(1,0,1))
portes(ans, NREP=100)
#
#Example 2
#Simulate a bivariate VARMA(1,0) process with length 300. 
k <- 2
n <- 300
Trunc.Series <-  50   
phi <-  array(c(0.5,0.4,0.1,0.5),dim=c(k,k,1))
theta <-  array(c(0,0.0,0,0),dim=c(k,k,1))
intercept <- c(10,12)
sigma <- matrix(c(1,0.71,0.71,2),k,k)
z<-simvarma(phi,theta=theta,sigma,intercept,n)
ans<-ar(z)
portes(ans, NREP=25) #NREP=25 is not enough for accurate p-values!
#
#Examples using snow or Rmpi. Takes a few minutes.
##############################################################
## The following script checks the residuals for randomness 
## Model VAR(11) fitted to house data after subtracting the mean. 
##
##
HouseData <- scale(house, scale = FALSE)
HOUSE.VAR11<-ar.ols(HouseData,aic=FALSE,intercept=FALSE,order.max=11)
res <- ts((HOUSE.VAR11$resid)[-(1:11), ])
#
## GVStat statistic on PC with one CPU (61.68 seconds)
portes(res) 
# 
## GVStat statistic on PC with 8 CPU's using "Rmpi" (10.44 seconds)
portes(res,statistic="GVStat",SpawnSlaves="Rmpi", nslaves=8)
#
## GVStat statistic on PC with 8 CPU's using "snow" (10.81 seconds)
portes(res,statistic="GVStat",SpawnSlaves="snow", nslaves=8)
##############################################################
## The following script generates Table 2 in Lin and McLeod (2008).
## It takes 1.96 minutes on PC with 8 CPU's using "Rmpi"
##
CRSP.AR5<- arima(CRSP, c(5,0,0))
NREP<- 1000
lags=c(10,20,30)
tb<-matrix(numeric(6*length(lags)),nrow=6)
tb[1,]<-portes(CRSP.AR5,lags=lags,statistic="GVStat",SpawnSlaves="Rmpi",
        nslaves=8, NREP=NREP,InfiniteVarianceQ=TRUE)[,2]
tb[2,]<-portes(CRSP.AR5,lags=lags,statistic="LiMcLeod",SpawnSlaves="Rmpi", 
        nslaves=8, NREP=NREP,InfiniteVarianceQ=TRUE)[,2]
tb[3,]<-portes(CRSP.AR5,lags=lags,statistic="GVStat",SpawnSlaves="Rmpi",
        nslaves=8, NREP=NREP)[,2]
tb[4,]<-portes(CRSP.AR5,lags=lags,statistic="LiMcLeod",SpawnSlaves="Rmpi",
        nslaves=8, NREP=NREP)[,2]
tb[5,]<-GVStat(CRSP.AR5,lags,5)[,4]
tb[6,]<-LiMcLeod(CRSP.AR5,lags,5)[,4]
rn <- c("GVStat-MC-Stable","LiMcLeod-MC-Stable", "GVStat-MC-Normal",
        "LiMcLeod-MC-Normal", "GVStat-asymptotic", "LiMcLeod-asymptotic")
dimnames(tb) <- list(rn, lags)
tb
#
#Output
#                            10          20          30
#GVStat-MC-Stable    0.06393606 0.034965035 0.021978022
#LiMcLeod-MC-Stable  0.05494505 0.019980020 0.022977023
#GVStat-MC-Normal    0.06293706 0.014985015 0.001998002
#LiMcLeod-MC-Normal  0.04995005 0.001998002 0.001998002
#GVStat-asymptotic   0.29111084 0.057389935 0.007760695
#LiMcLeod-asymptotic 0.04858500 0.002316690 0.002643823
##############################################################
## Fit AR(2) to Nile river data on PC with 8 CPU's
##
##
NILE.AR2 <- FitAR(Nile, 2)
lags <- c(5, 10, 20)
##				
## GVStat test on fitted model using "Rmpi" (5.9 seconds)
portes(res, lags, "GVStat",SpawnSlaves="Rmpi", nslaves=8) 
#
## LiMcLeod test on residuals using "snow" (5.95 seconds)
res <- NILE.AR2$res
portes(NILE.AR2, lags, "LiMcLeod",SpawnSlaves="snow", nslaves=8) 
##############################################################
## Test monthly log stock returns of Intel data for ARCH effects
## GVStat statistic on PC with 8 CPU's using "Rmpi" 
## It takes 5.93 seconds to get the results
##
data(monthintel)
returns <- as.ts(monthintel)
lags <- c(5, 10, 40)
portes(returns,lags,"GVStat",SpawnSlaves="Rmpi",nslaves=8,SquaredQ=TRUE) 
##############################################################
## Fit Fractional Gaussian Noise, FGN, to NileMin data in FGN package
## GVStat statistic on PC with 8 CPU's using "Rmpi"
##
library(FGN)
data(NileMin)
NILE.FGN <- FitFGN(NileMin)
lags <- c(5, 10, 20)
##				
## GVStat statistic on fitted model (55 seconds)
portes(NILE.FGN, lags, "GVStat",SpawnSlaves="Rmpi", nslaves=8) 
#
## GVStat statistic on residuals (6 seconds)
res <- NILE.FGN$res
portes(res, lags, "GVStat",SpawnSlaves="Rmpi", nslaves=8)