FitAR (version 1.94)

FitARz: Subset ARz Model Fitting

Description

The subset ARz model, defined by constraining partial autocorrelations to zero, is fitted using exact MLE. When length(p)=1, an AR(p) is fit by MLE.

Usage

FitARz(z, p, demean = TRUE, MeanMLEQ = FALSE, lag.max = "default")

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 ARz 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).

demean

TRUE, mean estimated. FALSE, mean is zero.

MeanMLEQ

use exact MLE for mean parameter

lag.max

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

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

The model and its properties are discussed in McLeod and Zhang (2006) and McLeod and Zhang (2008).

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, FitARp, GetFitARz, GetFitARpMLE, RacfPlot

Examples

#First Example: Fit exact MLE to AR(4) 
set.seed(3323)
phi<-c(2.7607,-3.8106,2.6535,-0.9238)
z<-SimulateGaussianAR(phi,1000)
ans<-FitARz(z,4,MeanMLEQ=TRUE)
ans
coef(ans)

## Not run: #save time building package
# #Second Example: compare with sample mean result
# ans<-FitARz(z,4)
# coef(ans)
# 
# #Third Example: Fit subset ARz 
# z<-log(lynx)
# FitARz(z, c(1,2,4,7,10,11))
# #now obain exact MLE for Mean as well
# FitARz(z, c(1,2,4,7,10,11), MeanMLE=TRUE)
# 
# #Fourth Example: Fit subset ARz
# somePACF<-c(0.5,0,0,0,-0.9)
# someAR<-PacfToAR(somePACF)
# z<-SimulateGaussianAR(someAR,1000)
# ans=FitARz(z, c(1,5),MeanMLEQ=TRUE)
# coef(ans)
# GetFitARz(z,c(1,5))#assuming a known zero mean
# ## End(Not run)