# setar: Self Threshold Autoregressive model In tsDyn: Nonlinear Time Series Models with Regime Switching

## Description

Self Exciting Threshold AutoRegressive model.

## Usage

 ```1 2 3 4 5``` ```setar(x, m, d=1, steps=d, series, mL, mM, mH, thDelay=0, mTh, thVar, th, trace=FALSE, nested=FALSE, include = c( "const", "trend","none", "both"), common=c("none", "include","lags", "both"), model=c("TAR", "MTAR"), ML=seq_len(mL), MM=seq_len(mM), MH=seq_len(mH),nthresh=1,trim=0.15, type=c("level", "diff", "ADF"), restriction=c("none","OuterSymAll","OuterSymTh") ) ```

## Arguments

 `x` time series `m, d, steps` embedding dimension, time delay, forecasting steps `series` time series name (optional) `mL,mM, mH` 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` 'time delay' for the threshold variable (as multiple of embedding time delay d) `mTh` coefficients for the lagged time series, to obtain the threshold variable `thVar` external threshold variable `th` threshold value (if missing, a search over a reasonable grid is tried) `trace` should additional infos be printed? (logical) `include` Type of deterministic regressors to include `common` Indicates which elements are common to all regimes: no, only the `include` variables, the lags or both `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 `model` Currently not implemented `nthresh` Number of threshold of the model `trim` trimming parameter indicating the minimal percentage of observations in each regime. Default to 0.15 `type` Whether the variable is taken is level, difference or a mix (diff y= y-1, diff lags) as in the ADF test `restriction` Restriction on the threshold. `OuterSymAll` will take a symmetric threshold and symmetric coefficients for outer regimes. OuterSymTh currently unavailable `nested` Whether is this a nested call? (useful for correcting final model df) `...` further arguments to be passed to `nlar`

## Details

Self Exciting Threshold AutoRegressive model.

x[t+steps] = ( phi1[0] + phi1[1] x[t] + phi1[2] x[t-d] + … + phi1[mL] x[t - (mL-1)d] ) I( z[t] <= th) + ( phi2[0] + phi2[1] x[t] + phi2[2] x[t-d] + … + phi2[mH] x[t - (mH-1)d] ) I( z[t] > th) + eps[t+steps]

with z the threshold variable. The threshold variable can alternatively be specified by (in that order):

thDelay

`z[t] = x[t - thDelay*d ]`

mTh

`z[t] = x[t] mTh[1] + x[t-d] mTh[2] + ... + x[t-(m-1)d] mTh[m]`

thVar

`z[t] = thVar[t]`

For fixed `th` and threshold variable, the model is linear, so `phi1` and `phi2` estimation can be done directly by CLS (Conditional Least Squares). Standard errors for phi1 and phi2 coefficients provided by the `summary` method for this model are taken from the linear regression theory, and are to be considered asymptoticals.

## Value

An object of class `nlar`, subclass `setar`

## Author(s)

Antonio, Fabio Di Narzo

## References

Non-linear time series models in empirical finance, Philip Hans Franses and Dick van Dijk, Cambridge: Cambridge University Press (2000).

Non-Linear Time Series: A Dynamical Systems Approach, Tong, H., Oxford: Oxford University Press (1990).

`plot.setar` for details on plots produced for this model from the `plot` generic.
 ```1 2 3 4 5 6 7 8``` ```#fit a SETAR model, with threshold as suggested in Tong(1990, p 377) mod.setar <- setar(log10(lynx), m=2, thDelay=1, th=3.25) mod.setar summary(mod.setar) ## example in Tsay (2005) data(m.unrate) setar(diff(m.unrate), ML=c(2,3,4,12), MH=c(2,4,12), th=0.1, include="none") ```