A note on the early warning system of change points : combination of regime switching and threshold models

Abrupt changes are a prevalent feature of financial data sets, such as prices of financial assets, returns of stocks, exchange rates, etc. An early warning system (EWS) can detect existing changes and predict possible future changes before they occur. Two important statistical models for change point detection and prediction are the regime-switching and threshold models. In the first model, the data set involves multiple structures that characterize the time series behaviours in different regimes. In a threshold model, change is detected as soon as a split variable passes a threshold. In this paper, by combining the two mentioned models, namely regime switching and threshold, an EWS for change point detection is designed. The underlying process for change detection obeys an AR(1) process. States are latent variables specifying whether a special time point is changed or not. They are realizations of the Markov chain. The predictive transition probabilities are determined by a threshold model based on adaptive recursive relations. This combination forms the mentioned EWS. Finally, two applications are given about change detection in stock returns and specifying business cycles.