SelectModel(FitAR) | R Documentation |
The AIC or BIC criterion is used to select the best fitting AR or subset AR model.
The result may be plotted using plot
.
SelectModel(z, lag.max = 15, SubsetModel = c("n", "p", "z"), method = "AIC", Best = 3, Candidates = 5)
z |
time series data |
lag.max |
maximum order of autoregression |
SubsetModel |
default is no subset. Alternatives are AR-phi or AR-zeta |
method |
default is AIC otherise is BIC |
Best |
number of models to be selected |
Candidates |
number of models initially selected using the approximate criterion |
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.
When 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 Best
>1.
If SubsetQ = FALSE, a matrix is return whose first column shows p and
second AIC or BIC.
Otherwise for subset select, the result is a list with q components, where q=BEST.
When method="AIC", the components in this list are:
p |
|
AIC |
{exact AIC}
Similarly when method="BIC", the second component is BIC
.
The components are arranged in order of the AIC/BIC criterion.
When SubsetModel="p" or "z", an attribute "model" indicating "ARp" or "ARz"
is included.
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.
For white noise, the best model is the null model, containing no lags. This is indicating by setting the model order, p=0.
A.I. McLeod
McLeod, A.I. and Zhang, Y. (2006). Partial autocorrelation parameterization for subset autoregression. Journal of Time Series Analysis, 27, 599-612.
plot.Selectmodel
,
PacfPlot
,
PacfPlot
,
FitAR
#Example 1: find a ARp subset model for lynx data using BIC z<-log(lynx) out<-SelectModel(z, SubsetModel="p", method="BIC", Best=5) plot(out) # #Example 2: find a ARz subset model for lynx data using BIC out<-SelectModel(z, SubsetModel="z", method="BIC", Best=5) plot(out) # #Example 3: Select AR(p) model out<-SelectModel(z, method="BIC", Best=5) out plot(out) # #Example 4: Fit subset models to lynx series z<-log(lynx) #requires library leaps. Should be automatically when FitAR package is loaded. pvec <- SelectModel(z, lag.max=11, SubsetModel="p", method="AIC", Best=1) ans1 <- FitARLS(z, pvec) pvec <- SelectModel(z, lag.max=11, SubsetModel="z", method="AIC", Best=1) ans2<-FitAR(z, pvec) summary(ans1) summary(ans2)