FitARp: Fit subset ARp Models
In FitAR: Subset AR Model Fitting

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

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.

1	FitARp(z, p, lag.max = "default", MLEQ = FALSE)

`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

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.

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

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, FitARz, GetFitARz, FitARp, GetFitARpMLE, RacfPlot

#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)

## Not run: #save time building package
#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

## End(Not run)

Loading required package: lattice
Loading required package: leaps
Loading required package: ltsa
Loading required package: bestglm
AR(4). MLE.
length of series = 1000 ,  number of parameters = 4
loglikelihood = -11.976 ,  AIC = 32 ,  BIC =  51.6
              MLE         sd     Z-ratio
phi(1)  2.7756178 0.01204356  230.464901
phi(2) -3.8317503 0.02691666 -142.356067
phi(3)  2.6691937 0.02691666   99.165105
phi(4) -0.9246365 0.01204356  -76.774352
mu      0.1027028 0.10140000    1.012848
AR(4). LS Fit.
length of series = 1000 ,  number of parameters = 4
loglikelihood = -12.246 ,  AIC = 32.5 ,  BIC =  52.1
              MLE         sd     Z-ratio
phi(1)  2.7711904 0.01239365  223.597684
phi(2) -3.8203730 0.02761804 -138.328921
phi(3)  2.6578437 0.02757072   96.400946
phi(4) -0.9193263 0.01234181  -74.488801
mu      0.1027028 0.10168537    1.010006
AR(11). MLE.
length of series = 114 ,  number of parameters = 6
loglikelihood = 89.164 ,  AIC = -166.3 ,  BIC =  -149.9 , UBIC =  -137.6
AR(11). LS Fit.
length of series = 114 ,  number of parameters = 6
loglikelihood = 89.001 ,  AIC = -166 ,  BIC =  -149.6 , UBIC =  -137.3
AR(11). LS Fit.
length of series = 114 ,  number of parameters = 5
loglikelihood = 89.006 ,  AIC = -168 ,  BIC =  -154.3 , UBIC =  -142.1