FitAR (version 1.94)

FitARp: Fit subset ARp Models

Description

The subset ARp is defined as an AR(p) in which some of the ar-coefficients are constrained to zero. This is the usual type of subset AR. In contrast the ARz model constrains some of the partial autocorrelation coefficients to zero.

Usage

FitARp(z, p, lag.max = "default", MLEQ = FALSE)

Arguments

z

time series, vector or ts object

p

p specifies the model. If length(p) is 1, an AR(p) is assumed and if p has length greater than 1, a subset ARp is assumed. For example, to fit a subset model with lags 1 and 4 present set p to c(1,4) or equivalently c(1,0,0,4). To fit a subset model with just lag 4, you must use p=c(0,0,0,4) since p=4 will fit a full AR(4).

lag.max

the residual autocorrelations are tabulated for lags 1, ..., lag.max. Also lag.max is used for the Ljung-Box portmanteau test.

MLEQ

TRUE, use MLE. FALSE, use LS

Value

A list with class name "FitAR" and components:

loglikelihood

value of the loglikelihood

phiHat

coefficients in AR(p) -- including 0's

sigsqHat

innovation variance estimate

muHat

estimate of the mean

covHat

covariance matrix of the coefficient estimates

zetaHat

transformed parameters, length(zetaHat) = \# coefficients estimated

RacfMatrix

residual autocorrelations and sd for lags 1, ..., lag.max

LjungBox

table of Ljung-Box portmanteau test statistics

SubsetQ

parameters in AR(p) -- including 0's

res

innovation residuals, same length as z

fits

fitted values, same length as z

pvec

lags used in AR model

demean

TRUE if mean estimated otherwise assumed zero

FitMethod

"MLE" or "LS"

IterationCount

number of iterations in mean mle estimation

convergence

value returned by optim -- should be 0

MLEMeanQ

TRUE if mle for mean algorithm used

ARModel

"ARp" if FitARp used, otherwise "ARz"

tsp

tsp(z)

call

result from match.call() showing how the function was called

ModelTitle

description of model

DataTitle

returns attr(z,"title")

z

time series data input

Details

Subset ARp model is fit using exact MLE. The built-in arima function is used for MLE. When MLEQ=FALSE, LS is used. LS is has been widely used in past for subset ARp fiting.

References

McLeod, A.I. and Zhang, Y. (2006). Partial Autocorrelation Parameterization for Subset Autoregression. Journal of Time Series Analysis, 27, 599-612.

McLeod, A.I. and Zhang, Y. (2008a). Faster ARMA Maximum Likelihood Estimation, Computational Statistics and Data Analysis 52-4, 2166-2176. DOI link: http://dx.doi.org/10.1016/j.csda.2007.07.020.

McLeod, A.I. and Zhang, Y. (2008b, Submitted). Improved Subset Autoregression: With R Package. Journal of Statistical Software.

See Also

FitAR, FitARz, GetFitARz, FitARp, GetFitARpMLE, RacfPlot

Examples

#First Example: Fit to AR(4) 
set.seed(3323)
phi<-c(2.7607,-3.8106,2.6535,-0.9238)
z<-SimulateGaussianAR(phi,1000)
#MLE using arima
ans1<-FitARp(z,4,MLEQ=TRUE)
ans1
coef(ans1)
#OLS
ans2<-FitARp(z,4,MLEQ=FALSE)
ans2
coef(ans2)

## Not run: #save time building package
# #Second Example: Fit subset ARp model
# z<-log(lynx)
# #MLE
# FitARp(z, c(1,2,4,7,10,11),MLEQ=TRUE)
# #LS
# FitARp(z, c(1,2,4,7,10,11),MLEQ=FALSE)
# 
# #Third Example: Use UBIC model selection to fit subset models
# z<-log(lynx)
# p<-SelectModel(z,ARModel="ARp")[[1]]$p
# #MLE #error returned by arima
# #ans1<-FitARp(z, p, MLEQ=TRUE)
# #ans1
# #LS
# ans2<-FitARp(z, p, MLEQ=FALSE)
# ans2
# ## End(Not run)