This thesis presents a time varying regime-switching model for US equity index daily returns. The parameters of the model are estimated recursively with the Kalman lter. We demonstrate our model and parameter estimation technique are effective by demonstrating improvements in model t compared to alternate models. Information from our model is used to build a Finite State Machine trading system with back-tested performance in excess of 15,000% above a buy and hold strategy for the DOW Jones Industrial average from 1928-2012. Similar results are found for both the S&P 500 index and the NASDAQ Composite index over a long period. Our model succeeds at identifying pro table investment opportunities and improving model t with a minimum of parameters.