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),
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 |
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. |
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).
See Also
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")