FitAR (version 1.94)

SelectModel: Select Best AR, ARz or ARp Model

Description

The AIC/BIC/UBIC/EBIC/BICq criterion is used to select the best fitting AR or subset AR model. When Best > 1, the result may be plotted using plot.

Usage

SelectModel(z, lag.max = 15, ARModel = c("AR", "ARz", "ARp"), Criterion = "default", Best = 3, Candidates = 5, t="default")

Arguments

z

time series data

lag.max

maximum order of autoregression

ARModel

"AR" for full AR(p) or "ARp"/"ARz" corresponding to subset models

Criterion

default is "BIC" for order selection and "BICq" for subset selection. Options: "AIC", "BIC", "UBIC", "EBIC", "BICq" and "GIC".

Best

final number of models to be selected

Candidates

number of models initially selected using the approximate criterion

t

tuning parameter, EBIC, BICq, GIC

Value

When $\code{Best} = 1$, a vector is returned indicated the lag or lags included in the model. The null model is indicated by returning 0 for the lag. An object with class "Selectmodel" is returned when $\code{Best} >1$. If ARModel = "AR", a matrix is return whose first column shows p and second AIC or BIC. Otherwise for subset selection, the result is a list with q components, where q=BEST. When Criterion = "UBIC", the components in this list are:

p

lags present, a 0 indicates the null model

UBIC

exact UBIC

similarly for the AIC/BIC case.The components are arranged in order of the criterion used.When ARModel = "ARp" or "ARz", an attribute "model" indicating "ARp" or "ARz" is included.

Warning

Setting Candidates too low can result in anomalous results. For example if Candidates = 1, we find that the top ranking model may depend on how large Best is set. This phenomenon is due to the fact that among the best AIC/BIC models there is sometimes very little difference in their AIC/BIC scores. Since the initial ranking of the Candidates is done using the approximate likelihood, the final ranking using the exact likelihood may change.

Details

McLeod and Zhang (2006) outline an approximate AIC/BIC selection algorithm. This algorithm is a refinement of that method. The refinement consists of automatically look for the best k candidates, where k = Candidates. Then the exact likelihood is evaluated for all k candidates. Out of these k candidates, the best q = Best are then selected. This two-step procedure is needed because if k is too low, the approximate AIC/BIC rankings may not agree with the exact rankings. This strategy is used for model selection for AR, ARz and ARp models. A plot method is available to graph the output. The UBIC and EBIC developed by Chen and Chen (2007) are an extension of the BIC criterion for subset selection. In the non-subset case UBIC is equivalent to BIC. The EBIC using a tuning parameter, G, where 0

References

McLeod, A.I. and Zhang, Y. (2006). Partial Autocorrelation Parameterization for Subset Autoregression. Journal of Time Series Analysis, 27, 599-612.

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

See Also

plot.Selectmodel, PacfPlot, PacfPlot, FitAR

Examples

#Example 1: Find an ARp subset model for lynx data using BIC
z<-log(lynx)
out<-SelectModel(z, ARModel="ARp", Criterion="BIC", Best=5)
plot(out)
#
#Example 2: Find an ARz subset model for lynx data using BIC
out<-SelectModel(z, ARModel="ARz", Criterion="BIC", Best=5)
plot(out)
#
#Example 3: Select an AR(p) model
out<-SelectModel(z, ARModel="AR", Criterion="BIC", Best=5)
out
plot(out)
out<-SelectModel(z, ARModel="AR", Criterion="BIC", Best=1)
#
#Example 4: Fit subset models to lynx series
z<-log(lynx)
#requires library leaps. Should be automatically when FitAR package is loaded.
#first fit ARp
pvec <- SelectModel(z, lag.max=11, ARModel="ARp", Criterion="AIC", Best=1)
ans1 <- FitAR(z, pvec, ARModel="ARp", MLEQ=FALSE)
#now fit ARz
pvec <- SelectModel(z, lag.max=11, ARModel="ARz", Criterion="AIC", Best=1)
ans2<-FitAR(z, pvec, ARModel="ARz")
#compare
summary(ans1)
summary(ans2)
#Use UBIC
pvec <- SelectModel(z, ARModel="ARp",lag.max=11,Best=1)
ans3<-FitAR(z, pvec, ARModel="ARp")
pvec <- SelectModel(z, ARModel="ARz",lag.max=11,Best=1)
ans4<-FitAR(z, pvec, ARModel="ARz")
#compare
summary(ans3)
summary(ans4)
#
#Example 5: lynx data subset AR models
#The AIC and BIC choose the same models as the GIC with t=0.1 and t=0.01 respectively.
#An even more parsimonious model is chosen with t=0.001
SelectModel(z, lag.max=15, ARModel="ARp", Criterion="GIC", Best=1, Candidates=5, t=0.1)
SelectModel(z, lag.max=15, ARModel="ARp", Criterion="GIC", Best=1, Candidates=5, t=0.01)
SelectModel(z, lag.max=15, ARModel="ARp", Criterion="GIC", Best=1, Candidates=5, t=0.001)
ans<-SelectModel(z, lag.max=15, ARModel="ARp", Criterion="GIC", Best=3, Candidates=5, t=0.001)
plot(ans)