selectSETAR {tsDyn}R Documentation

Automatic selection of SETAR hyper-parameters

Description

Automatic selection of SETAR hyper-parameters

Usage

selectSETAR(x, m, d=1, steps=d, series, mL, mH,mM, thDelay=0, mTh, thVar, th=MakeThSpec(), trace=TRUE, include = c("const", "trend","none", "both"), common=c("none", "include","lags", "both"), model=c("TAR", "MTAR"), ML=seq_len(mL),MH=seq_len(mH), MM=seq_len(mM),nthresh=1,trim=0.15,criterion = c("pooled-AIC", "AIC","BIC", "SSR"),thSteps = 7,  plot=TRUE,max.iter=2, type=c("level", "diff", "ADF"), same.lags=FALSE, restriction=c("none","OuterSymAll","OuterSymTh"))

Arguments

x time series
m, d, steps embedding parameters. For their meanings, see help about nlar
series time series name (optional)
mL, mH,mM autoregressive order for ‘low’ (mL) ‘middle’ (mM, only useful if nthresh=2) and ‘high’ (mH)regime (default values: m). Must be <=m. Alternatively, you can specify ML
thDelay Vector of possible ‘threshold delay’ values to check for
mTh coefficients for the lagged time series, to obtain the threshold variable
thVar external threshold variable
th Different specifications of the grid search, to pre-specify a value or set the number of points to search. SeeMakeThSpec
trace should additional infos be printed? (logical)
include Type of deterministic regressors to include
common Indicates which elemenst are common to all regimes: no, only the include variables, the lags or both
model Currently not implemented
ML,MM,MH vector of lags for order for ‘low’ (ML) ‘middle’ (MM, only useful if nthresh=2) and ‘high’ (MH)regime. Max must be <=m
nthresh Number of threshold of the model
trim trimming parameter indicating the minimal percentage of observations in each regime. Default to 0.15
criterion Model selection criterion
thSteps Not used
plot Should a plot showing the criterion values be printed? (logical)
max.iter Number of iterations for the alogorithm
type Whether the variable is taken is level, difference or a mix (diff y= y-1, diff lags) as in the ADF test
same.lags Logical. When AIC or pooled-AIC is used and arg m is given, should it search for same number of lags in each regime (TRUE) or allow for different (FALSE) lags in each regime. Different lags involves more computation
restriction Restriction on the threshold. OuterSymAll will take a symmetric threshold and symmetric coefficients for outer regimes. OuterSymTh currently unavailable

Details

Routine for automatic selection of SETAR models hyper parameters.

An exhaustive search over all possible combinations of values of specified hyper-parameters is performed. Thus the threshold delay, the number of lags in each regime and the threshold value are computed.

Embedding parameters d,steps are kept fixed.

Possible criteria are the usual SSR, AIC and a pooled AIC formula: AIC(low regime model) + AIC(high regime model). The default criterion is the pooled AIC formula. SSR criterion can't be used to compare models with different lags.

When two thresholds(nthresh=2) have to be computed, the search for the second is made conditional on results for first threshold as suggested in Gonzalo and Pittarakis (2002). Refinements can be obtained by using max.iter (first threshold being restimated based on the second one). If SSR is used, the number of lags in the inner regime is either the same if only arg m was given, otherwise it has to be pre-specified. Criterion AIC can be used to determine the number of lags in the nner regime, whereas pooled-aic is currently not implemented for nthresh=2.

By default, all threshold values excluding the upper and lower trim of the threshold values are taken as potential threshold. restriction can be made with arg th. See function MakeThSpec.

Value

An object of class selectSETAR (print and plot methods) with:

res A data-frame, with columns giving hyper-parameter values and the computed AIC for each row (only the best 10/5s are returned)
res2 Same as res, returned if ntresh=2 otherwise set to NULL
bests estimated hyper-parameters
th, firstBests, bests2th, ML, MM, MH estimated parameters, from first and conditional search
criterion, nthresh,same.lags returns args given by user
allTh all threshold values and correspoinding criterion from first search

Author(s)

Antonio, Fabio Di Narzo and Stigler, Matthieu

References

Gonzalo, J. & Pitarakis, J. (2002) Estimation and model selection based inference in single and multiple threshold models, Journal of Econometrics, 110, 319 - 352

See Also

selectLSTAR, selectNNET, MakeThSpec

Examples

llynx <- log10(lynx)
selectSETAR(llynx, m=2)
#Suggested model is the following:
setar(llynx, m=2, thDelay=1, th=3.4)

[Package tsDyn version 0.7-1 Index]