ON CONTINUOUS-TIME THRESHOLD AUTOREGRESSION

doi:10.1016/0169-2070(92)90116-Q

ON CONTINUOUS-TIME THRESHOLD AUTOREGRESSION

1992-10-01

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DOI：10.1016/0169-2070(92)90116-Q

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The use of non-linear models in time series analysis has expanded rapidly in the last ten years, with the development of several useful classes of discrete-time non-linear models. One family of processes which has been found valuable is the class of self-exciting threshold autoregressive (SETAR) models discussed extensively in the books of Tong (1983, 1990). In this paper we consider problems of modelling and forecasting with continuous-time threshold autoregressive (CTAR) processes. Techniques for analyzing such models have been proposed by Tong and Yeung (1991) and Brockwell, Hyndman and Grunwald (1991). In this paper we define a CTAR(p) process {X(t)} with boundary width 2delta > 0 as the first component of a p-dimensional Markov process {X(t)}, defined by a stochastic differential equation. We are primarily concerned with the problems of model-fitting and forecasting when observations are available at times 1, 2, . . . , N; however, the techniques considered apply equally well to irregularly spaced observations. For practical computations with CTAR processes we approximate the process {X(t)} by a linearly interpolated discrete-time Markov process whose transitions occur at times j/n, j = 1, 2, . . . , with n large. This model is used to fit 'narrow boundary' CTAR models to both simulated and real data.

Keywords:

NONLINEAR FORECASTING

THRESHOLD AUTOREGRESSION

STATE SPACE REPRESENTATION

MAXIMUM LIKELIHOOD ESTIMATION

CONTINUOUS-TIME AUTOREGRESSION

ON CONTINUOUS-TIME THRESHOLD AUTOREGRESSION

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