SETAR {tsDyn} R Documentation

## Self Threshold Autoregressive model

### Description

Self Exciting Threshold AutoRegressive model.

### Usage

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),
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 Whether the threshold variable is taken in levels (TAR) or differences (MTAR) 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)

### Details

Self Exciting Threshold AutoRegressive model.

X_{t+s} = x_{t+s} = ( \phi_{1,0} + \phi_{1,1} x_t + \phi_{1,2} x_{t-d} + \dots + \phi_{1,mL} x_{t - (mL-1)d} ) I( z_t \leq th) + ( \phi_{2,0} + \phi_{2,1} x_t + \phi_{2,2} x_{t-d} + \dots + \phi_{2,mH} x_{t - (mH-1)d} ) I(z_t > th) + \epsilon_{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 asymptotical.

### 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.

### Examples

#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")


[Package tsDyn version 11.0.4.1 Index]