Self Exciting Threshold AutoRegressive model.
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") )An object of class nlar, subclass setar
time series
embedding dimension, time delay, forecasting steps
time series name (optional)
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
'time delay' for the threshold variable (as multiple of embedding time delay d)
coefficients for the lagged time series, to obtain the threshold variable
external threshold variable
threshold value (if missing, a search over a reasonable grid is tried)
should additional infos be printed? (logical)
Type of deterministic regressors to include
Indicates which elements are common to all regimes: no, only the include variables, the lags or both
vector of lags for order for ‘low’ (ML) ‘middle’ (MM, only useful if nthresh=2) and ‘high’ (MH)regime. Max must be <=m
Whether the threshold variable is taken in levels (TAR) or differences (MTAR)
Number of threshold of the model
trimming parameter indicating the minimal percentage of observations in each regime. Default to 0.15
Whether the variable is taken is level, difference or a mix (diff y= y-1, diff lags) as in the ADF test
Restriction on the threshold. OuterSymAll will take a symmetric threshold and symmetric coefficients for outer regimes. OuterSymTh currently unavailable
Whether is this a nested call? (useful for correcting final model df)
Antonio, Fabio Di Narzo
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):
z[t] = x[t - thDelay*d ]
z[t] = x[t] mTh[1] + x[t-d] mTh[2] + ... + x[t-(m-1)d] mTh[m]
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.
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.
#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")
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