portes (version 1.04)

portes-package: Portmanteau Tests for ARMA, VARMA, ARCH, and FGN Models

Description

This package contains a set of portmanteau diagnostic checks for univariate and multivariate time series, based on the chi-square asymptotic distribution and the parametric bootstrap significance level. It can be used for simulating data from ARMA or VARMA Models.

Parametric Bootstrap Portmanteau Test

The main function in this package, portes, works with univariate and multivariate time series. It implements the parametric bootstrap versions of the generalized variance test as described by Lin and McLeod (2006), Mahdi and McLeod (2010), and the modified test given by Li and McLeod (1981) (See the argument statistic=c("GVStat","LiMcLeod") in portes function). The generalized variance portmanteau test is implemented in this package with the name GVStat, while the other one has the name LiMcLeod. Both tests, GVStat and LiMcLeod can be used for univariate and multivariate time series. For faster calculations, users that have PC's with multiple CPU's may take advantage of implementing the parallel computing techniques in portes function after downloading either Rmpi or snow. The default argument in portes function, SpawnSlaves=c("default","Rmpi","snow"), implements the parametric bootstrap test on PC's with only one CPU's. The snow R package is available on CRAN with more details in the link http://www.stat.uiowa.edu/~luke/R/cluster/cluster.html. Instructions to install and run Rmpi package under Windows is given in the link http://www.stats.uwo.ca/faculty/yu/Rmpi/windows.htm. More information about parallel computing with R is provided by http://cran.r-project.org/web/views/HighPerformanceComputing.html. parametric bootstrap test for usual residuals{ The default arguments in the function portes corresponds to parametric bootstrap test for the usual residuals. } parametric bootstrap test for squared residuals, ARCH effects{ By setting the argument SquaredQ = TRUE in portes function, the parametric bootstrap test for ARCH effects will be implemented. } parametric bootstrap test for residuals with infinite variances{ By setting the argument InfiniteVarianceQ = TRUE in portes function, the parametric bootstrap test for residuals with infinite variance will be implemented. } parametric bootstrap test for FGN{ After fitting FGN model using the function FitFGN in the FGN R package, the output will be an object with a class "FitFGN". By substituting this object as a first entry in the portes function, the parametric bootstrap test for FGN model will be implemented. }

Simulate Data From <code>ARMA</code> or <code>VARMA</code>

The function simvarma in this package is very useful for simulating data from ARMA or VARMA with innovations follow Gaussian or stable Paretian distribution. The default argument of simvarma function, StableParameters=NA, is used for Gaussian innovations. For innovations from stable Paretian distribution with stable parameters ALPHA, BETA, GAMMA, and DELTA, the argument StableParameters is setting to equal to these parameters values.

Details

ll{ Package: portes Type: Package Version: 1.04 Date: 2010-09-08 LazyLoad: yes LazyData: yes Depends: FitAR, akima Suggests: FGN, snow, rlecuyer Recommends: Rmpi Classification/ACM: G.3, G.4, I.5.1 Classification/MSC: 62M10, 91B84 License: GPL (>= 2) }

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. McCulloch, J. H. (1986). "Simple Consistent Estimator of Stable Distribution Parameters". Commun. Statist.--Simula., 15(4), 1109-1136. McLeod AI, Li WK (1983). "Distribution of the Residual Autocorrelation in Multivariate ARMA Time Series Models". Journal of Time Series Analysis, 4, 269-273. McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007). "Algorithms for Linear Time Series Analysis". Journal of Statistical Software.

Examples

#########################################################################
## parametric bootstrap test for usual residuals ##
#########################################################################
data("DEXCAUS")
returns <- log(DEXCAUS[-1]/DEXCAUS[-length(DEXCAUS)])
portes(returns)

data("house")
HouseData <- scale(house, scale = FALSE)
HOUSE.VAR11<- ar.ols(HouseData,aic=FALSE,intercept=FALSE,order.max=11)
res <- ts((HOUSE.VAR11$resid)[-(1:11), ])
portes(res, SpawnSlaves="snow")
#########################################################################
## parametric bootstrap test for squared residuals, ARCH effects ##
#########################################################################
data("monthintel")
returns <- as.ts(monthintel)
lags <- c(5, 10, 40)
portes(returns,lags,"GVStat",SpawnSlaves="Rmpi",nslaves=8,SquaredQ=TRUE)
#########################################################################
## parametric bootstrap test for residuals with infinite variances ##
#########################################################################
data("CRSP")
CRSP.AR5<- arima(CRSP, c(5, 0, 0))
NREP<- 1000
lags=c(10, 20, 30)
portes(CRSP.AR5, lags = lags, statistic = "GVStat", SpawnSlaves = "Rmpi",
        nslaves = 8, NREP = NREP, InfiniteVarianceQ = TRUE)      
#########################################################################
## parametric bootstrap test for FGN ##
#########################################################################
library("FGN")
data("NileMin")
NILE.FGN <- FitFGN(NileMin)
lags <- c(5, 10, 20)
portes(NILE.FGN, lags, "GVStat", SpawnSlaves = "Rmpi", nslaves = 8) 
#########################################################################
## Simulate a VARMA process with innovations that have finite variance ##
#########################################################################
n <- 300
phi <-  array(c(0.5, 0.4, 0.1, 0.5),dim = c(2, 2, 1))
theta <-  array(c(0, 0.25, 0, 0),dim = c(2, 2, 1))
intercept <- c(1, 2)
sigma <- matrix(c(1, 0.71, 0.71, 2), 2, 2)
simvarma(phi, theta, sigma, intercept, n)
#########################################################################
## Simulate a VARMA process with innovations that have infinite variance#
#########################################################################
n <- 300
phi <-  array(c(0.5, 0.4, 0.1, 0.5),dim = c(2, 2, 1))
theta <-  array(c(0, 0.25, 0, 0),dim = c(2, 2, 1))
intercept <- c(1, 2)
sigma <- matrix(c(1, 0.71, 0.71, 2), 2, 2)
ALPHA <- c(1.3, 1.6)
BETA <- c(0, 0.2)
GAMMA <- c(1, 1)
DELTA <- c(0, 0.2)
StableParameters <- c(ALPHA, BETA, GAMMA, DELTA)
simvarma(phi, theta, sigma, intercept, n, StableParameters)