tsDyn (version 0.7-60)

SETAR: Self Threshold Autoregressive model

Description

Self Exciting Threshold AutoRegressive model.

Usage

setar(x, m, d=1, steps=d, series, mL=m, mH=m, thDelay=0, th,
trace=FALSE,include = c( "const", "trend","none", "both"),
common=FALSE, model=c("TAR", "MTAR"), ML=seq_len(mL), MH=seq_len(mH),nthresh=1,trim=0.15,
 type=c("level", "diff", "ADF"), restriction=c("none","OuterSymAll","OuterSymTh") )
setar(x, m, d=1, steps=d, series, mL=m, mH=m, mTh, th,
trace=FALSE,include = c( "const", "trend","none", "both"), 
common=FALSE, model=c("TAR", "MTAR"), ML=seq_len(mL), MH=seq_len(mH),nthresh=1,trim=0.15, 
type=c("level", "diff", "ADF"), restriction=c("none","OuterSymAll","OuterSymTh") )
setar(x, m, d=1, steps=d, series, mL=m, mH=m, thVar, th,
trace=FALSE,include = c( "const", "trend","none", "both"), 
common=FALSE, model=c("TAR", "MTAR"), ML=seq_len(mL), 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,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 resonable grid is tried)

trace

should additional infos be printed? (logical)

include

Type of deterministic regressors to include

common

Indicates which elemenst are common to all regimes: no, only the include variables, the lags or both

ML,MH

vector of lags for order for low (ML) middle (MM, only useful if nthresh=2) and high (MH)regime. Max must be

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= 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

...

further arguments to be passed to nlar

Value

• An object of class nlar, subclass setar

synopsis

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") )

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 treshold variable. The threshold variable can alternatively be specified by (in that order): [object Object],[object Object],[object Object] 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.

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)

if(require(FinTS)) {
	data(m.unrate)
	setar(diff(m.unrate), ML=c(2,3,4,12), MH=c(2,4,12), th=0.1, include="none")
}