tsDyn (version 0.7-60)

LSTAR: Logistic Smooth Transition AutoRegressive model

Description

Logistic Smooth Transition AutoRegressive model.

Usage

lstar(x, m, d=1, steps=d, series, mL, mH, thDelay, 
          th, gamma, trace=TRUE, control=list())
lstar(series, m, d, steps, mL, mH, mTh,
    th, gamma, trace=TRUE, control=list())
lstar(series, m, d, steps, mL=m, mH=m, thVar,
    th, gamma, trace=TRUE, control=list())

Arguments

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

mH

autoregressive order for 'high' regime (default: m). Must be

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, gamma

starting values for coefficients in the LSTAR model. If missing, a grid search is performed

trace

should additional infos be printed? (logical)

control

further arguments to be passed as control list to optim

Value

• An object of class nlar, subclass lstar, i.e. a list with fitted model informations.

synopsis

lstar(x, m, d=1, steps=d, series, mL, mH, mTh, thDelay, thVar, th, gamma, trace=TRUE, control=list())

Details

$$x_{t+s} = ( \phi_{1,0} + \phi_{1,1} x_t + \phi_{1,2} x_{t-d} + \dots + \phi_{1,mL} x_{t - (mL-1)d} ) G( z_t, th, \gamma ) + ( \phi_{2,0} + \phi_{2,1} x_t + \phi_{2,2} x_{t-d} + \dots + \phi_{2,mH} x_{t - (mH-1)d} ) (1 - G( z_t, th, \gamma ) ) + \epsilon_{t+steps}$$ with z the treshold variable, and $G$ the logistic function, computed as plogis(q, location = th, scale = 1/gamma), so see plogis documentation for details on the logistic function formulation and parameters meanings. The threshold variable can alternatively be specified by: [object Object],[object Object],[object Object]

Note that if starting values for phi1 and phi2 are provided, isn't necessary to specify mL and mH. Further, the user has to specify only one parameter between mTh, thDelay and thVar for indicating the threshold variable.

Estimation is done by analytically determining phi1 and phi2 (through linear regression) and then minimizing residuals sum of squares with respect to th and gamma. These two steps are repeated until convergence is achieved. For the nonlinear estimation of the parameters th and gamma, the program uses the optim function, with its default optimization method. You can pass further arguments directly to the 'control' list argument of this function. For istance, the option maxit maybe useful when there are convergence issues (see examples).

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.lstar for details on plots produced for this model from the plot generic.

Examples

#fit a LSTAR model. Note 'maxit': slow convergence
mod.lstar <- lstar(log10(lynx), m=2, mTh=c(0,1), control=list(maxit=3000))
mod.lstar