Prediction of financial time series with hidden Markov models.

摘要

In this thesis, we develop an extension of the Hidden Markov Model (HMM) that addresses two of the most important challenges of financial time series modeling: non-stationary and non-linearity. Specifically, we extend the HMM to include a novel exponentially weighted Expectation-Maximization (EM) algorithm to handle these two challenges. We show that this extension allows the HMM algorithm to model not only sequence data but also dynamic financial time series. We show the update rules for the HMM parameters can be written in a form of exponential moving averages of the model variables so that we can take the advantage of existing technical analysis techniques. We further propose a double weighted EM algorithm that is able to adjust training sensitivity automatically. Convergence results for the proposed algorithms are proved using techniques from the EM Theorem.;Experimental results show that our models consistently beat the S&P 500 Index over five 400-day testing periods from 1994 to 2002, including both bull and bear markets. Our models also consistently outperform the top 5 S&P 500 mutual funds in terms of the Sharpe Ratio.