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

time series, vector or ts object

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

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.

Examples

Run this code

#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)

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