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

## Description

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.

## Usage

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

## 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 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

## Details

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.

## 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

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.

`FitAR`, `FitARz`, `GetFitARz`, `FitARp`, `GetFitARpMLE`, `RacfPlot`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ```#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")[]\$p #MLE #error returned by arima #ans1<-FitARp(z, p, MLEQ=TRUE) #ans1 #LS ans2<-FitARp(z, p, MLEQ=FALSE) ans2 ## End(Not run) ```

### Example output

```Loading required package: lattice
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
```

FitAR documentation built on May 2, 2019, 3:22 a.m.