SETAR {tsDyn} | R Documentation |
Self Exciting Threshold AutoRegressive model.
setar(x, m, d=1, steps=d, series, mL=m, mH=m, thDelay=0, th, trace=FALSE) setar(x, m, d=1, steps=d, series, mL=m, mH=m, mTh, th, trace=FALSE) setar(x, m, d=1, steps=d, series, mL=m, mH=m, thVar, th, trace=FALSE)
x |
time series |
m, d, steps |
embedding dimension, time delay, forecasting steps |
series |
time series name (optional) |
mL |
autoregressive order for 'low' regime (dafult: m). Must be <=m |
mH |
autoregressive order for 'high' regime (default: m). Must be <=m |
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 resonable grid is tried) |
trace |
should additional infos be printed? (logical) |
... |
further arguments to be passed to nlar |
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 treshold 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 asymptoticals.
An object of class nlar
, subclass setar
Antonio, Fabio Di Narzo
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) mod.setar <- setar(log10(lynx), m=2, thDelay=1, th=3.25) mod.setar summary(mod.setar)