State switching in US equity index returns based on SETAR model with Kalman filter tracking

This paper develops a new self-excited threshold autoregressive model (SETAR) for US equity Index returns modeling and analysis. First, a two regime switching model is formulated. The regime state is controlled by a simple piecewise function of lagged values from the time series itself. The hypothesis test is conduct to verify the statistical significance of two regimes in stock index returns. Then a new state space model with time-varying parameters is developed to model the market dynamics. The Kalman filter is used for model estimation and return prediction. Based on Kalman filter predication, a Finite State Machine (FSM) trading system based on the model predictions is presented as a practical application of the model. The effectiveness of this new model is illustrated for the DOW Jones Industrial Average (DJIA) and S&P 500 return series over a long period.