Modeling temporal structure of time series with hidden markov experts

Le résumé fourni par la source

This thesis explored using hidden Markov models for modeling time series and applied the model to both point forecasting and density forecasting. Traditionally, hidden Markov models are used in speech recognition, where predictions are not concerned. In this thesis, we used the algorithm to do both point forecasting and density forecasting. This thesis contains both theoretical and empirical analysis of the methods. The studies lead to the understanding of the method's behavior and possible applications to financial time series. Hidden Markov Experts extend directly from hidden Markov models. In the proposed model, each expert can be linear or nonlinear. Based on the likelihood function, we discussed the EM algorithm for Hidden Markov Experts. We used the model in point forecasting and in regime recovering. For the computer simulated data, the new algorithm found the correct parameters and recovered the regimes that generating the data. Compared to the gated experts, the new approach is more powerful in modeling regime switching time series. The new algorithm is also applied to real world financial data: modeling both high frequency foreign exchange data and daily S&P500 data. The regimes retrieved by Hidden Markov Experts were found to be corresponding to the volatility clustering. This makes further applications of Hidden Markov Experts in option pricing a very interesting topic for future study. Hidden Markov Experts are also used to predict the conditional density of time series. Switching models were mainly used in economic field to predict only the conditional mean of time series. In this thesis, we applied Hidden Markov Experts to construct the density forecasts by assuming the density is mixture of Gaussians. From the simulated experiment, we can see that hidden Markov experts can predict the density correctly under the criteria of probability integral transform method. We also applied this approach to the S&P 500 data. It is important to see that even it is hard to predict to conditional mean, the algorithm still significantly improves the forecasts of density.

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