FitARz: Subset ARz Model Fitting
In FitAR: Subset AR Model Fitting

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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.

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

`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.

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

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)

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

A.I. McLeod

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.

FitAR, FitARp, GetFitARz, GetFitARpMLE, RacfPlot

#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)