Self Threshold Autoregressive model
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 
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 
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= y1, diff lags) as in the ADF test 
restriction 
Restriction on the threshold. 
nested 
Whether is this a nested call? (useful for correcting final model df) 
... 
further arguments to be passed to 
Details
Self Exciting Threshold AutoRegressive model.
x[t+steps] = ( phi1[0] + phi1[1] x[t] + phi1[2] x[td] + … + phi1[mL] x[t  (mL1)d] ) I( z[t] <= th) + ( phi2[0] + phi2[1] x[t] + phi2[2] x[td] + … + phi2[mH] x[t  (mH1)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[td] mTh[2] + ... + x[t(m1)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
Nonlinear time series models in empirical finance, Philip Hans Franses and Dick van Dijk, Cambridge: Cambridge University Press (2000).
NonLinear Time Series: A Dynamical Systems Approach, Tong, H., Oxford: Oxford University Press (1990).
See Also
plot.setar
for details on plots produced for this model from the plot
generic.
Examples
1 2 3 4 5 6 7 8 9 