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Approximations and boundary conditions for continuous-time threshold autoregressive processes

Part of: Stochastic analysis Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Rob J. Hyndman
Rob J. Hyndman*
Affiliation:
The University of Melbourne
*
∗Postal address: Department of Statistics, University of Melbourne, Parkville, V1C 3052, Australia.
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Abstract

Continuous-time threshold autoregressive (CTAR) processes have been developed in the past few years for modelling non-linear time series observed at irregular intervals. Several approximating processes are given here which are useful for simulation and inference. Each of the approximating processes implicitly defines conditions on the thresholds, thus providing greater understanding of the way in which boundary conditions arise.

Keywords

CONTINUOUS-TIME AUTOREGRESSIONTHRESHOLD AUTOREGRESSIONNON-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONSUNEQUALLY SPACED TIME SERIES

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1103 - 1109
Copyright
Copyright © Applied Probability Trust 1994 

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