Approximations and boundary conditions for continuous time threshold autoregressive processes

Rob J Hyndman
(1994) Journal of Applied Probability, 31(4), 1103-1109


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 autoregression, threshold autoregression, non-linear stochastic differential equations, unequally spaced time series.