setar: Self Threshold Autoregressive model

In tsDyn: Nonlinear Time Series Models with Regime Switching

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 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 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 include variables, the lags or both
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. OuterSymAll will take a symmetric threshold and symmetric coefficients for outer regimes. OuterSymTh currently unavailable
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")

tsDyn documentation built on Oct. 31, 2024, 5:08 p.m.