Fit subset ARp Models
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.
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.
#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)
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