FitAR (version 1.94)

GetLeapsAR: Select lags for Best Subset ARp Model

Description

The subset ARp model is the usual subset model, for example see Tong (1977). This function is used by SelectModel for model identification for ARp models.

Usage

GetLeapsAR(z, lag.max = 15, Criterion = "UBIC", Best = 3, Candidates=5, t="default", ExactQ=FALSE)

Arguments

z

ts object or vector containing time series

lag.max

maximum order of the AR

Criterion

default UBIC, other choices are "AIC", "BIC", "EBIC", "BICq", "GIC"

Best

the number of based selected. Ignore with "GIC".

Candidates

number of models initially selected using the approximate criterion

t

tuning parameter, EBIC, BICq, GIC

ExactQ

exhaustive numeration using exact likelihood. Still under under development. NOT AVAILABLE IN THIS VERSION

Value

When 'Criterion' is one of UBIC, AIC, BIC, EBIC, BICq, a list with components:

p

lags present in model

UBIC

approximate UBIC (Chen & Chen, 2007), if Criterion=="UBIC"

AIC

approximate AIC (McLeod and Zhang, 2006a, eqn. 15), if Criterion=="AIC"

BIC

approximate BIC (McLeod and Zhang, 2006a, eqn. 15), if Criterion=="BIC"

EBIC

approximate EBIC (McLeod and Zhang, 2006a, eqn. 15), if Criterion=="EBIC"

BICq

approximate BICq, if Criterion=="BICq"

GIC

approximate GIC, if Criterion=="GIC"

Warning

AIC and BIC values produced are not comparable to AIC and BIC produced by SelectModel for ARz models. However comparable AIC/BIC values are produced when the selected models are fit by FitAR.

Details

The R function leaps in the R package leaps is used to compute the subset regression model with the smallest residual sum of squares containing 1, ..., lag.max parameters. The mean is always included, so the only parameters considered are the phi coefficients. After the best models containing 1, ..., lag.max parameters are selected the models are individually refit to determine the exact likelihood function for each selected model. Based on this likelihood the UBIC/BIC/AIC is computed and then the best models are selected. The UBIC criterion was developed by Chen and Chen (2007). The EBIC using a tuning parameter, G, where 0

References

Tong, H. (1977) Some comments on the Canadian lynx data. Journal of the Royal Statistical Society A 140, 432-436.

Chen, J. and Chen, Z. (2008). Extended Bayesian Information Criteria for Model Selection with Large Model Space. Biometrika.

Changjiang Xu and A. I. McLeod (2010). Bayesian information criterion with Bernoulli prior. Submitted for publication.

Changjiang Xu and A. I. McLeod (2010). Model selection using generalized information criterion. Submitted for publication.

See Also

SelectModel, GetFitARpLS, leaps

Examples

#Example 1: Simple Example
#for the log(lynx) Tong (1977) selected an ARp(1,2,4,10,11)
#using the AIC and a subset selection algorithm. Our more exact
#approach shows that the ARp(1,2,3,4,10,11) has slightly lower
#AIC (using exact likelihood evaluation).  
z<-log(lynx)
GetLeapsAR(z, lag.max=11)
GetLeapsAR(z, lag.max=11, Criterion="BIC")

#Example 2: Subset autoregression depends on lag.max!
#Because least-squares is used, P=lag.max observations are
#  are deleted. This causes different results depending on lag.max.
#This phenomenon does not happen with "ARz" subset models
#ARp models depend on lag.max
GetLeapsAR(z, lag.max=15, Criterion="BIC")
GetLeapsAR(z, lag.max=20, Criterion="BIC")

#Example 3: Comparing GIC with BIC, AIC, UBIC and BICq
z <- log(lynx)
GetLeapsAR(z, lag.max=15, Criterion="BIC", Best=1)
GetLeapsAR(z, lag.max=15, Criterion="AIC", Best=1)
GetLeapsAR(z, lag.max=15, Criterion="UBIC", Best=1)
GetLeapsAR(z, lag.max=15, Criterion="BICq", Best=1, t=0.25)
GetLeapsAR(z, lag.max=15, Best=1, Criterion="GIC", t=0.01)
ans<-GetLeapsAR(z, lag.max=15, Best=3, Criterion="GIC", t=0.001)
plot(ans)