FitARz {FitAR}R Documentation

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.

Details

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

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)

Note

Normally one would use the FitAR function which then calls this function for the ARz case.

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, 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)

#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

[Package FitAR version 1.74 Index]