APPROXIMATIONS AND BOUNDARY-CONDITIONS FOR CONTINUOUS-TIME THRESHOLD AUTOREGRESSIVE PROCESSES

Continuous-time threshold autoregressive (CTAR) processes have been de veloped in the past few years for modelling non-linear time series obs erved at irregular intervals. Several approximating processes are give n here which are useful for simulation and inference. Each of the appr oximating processes implicitly defines conditions on the thresholds, t hus providing greater understanding of the way in which boundary condi tions arise.