FitARp {FitAR}R Documentation

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

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.

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

Author(s)

A.I. McLeod

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)

#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

[Package FitAR version 1.74 Index]