Financial time series prediction using Kalman Filters and Hidden Markov models

Abstract

Financial markets are challenging targets for analysis and prediction. The existence of many factors that contribute to a nal price of security at time t, makes the task of predicting a future price a very hard task indeed. In the past, many statistical and non-statistical models have been utilized that attempted to perform this daunting task - the aim of this thesis is going to be trying to demonstrate Hidden Markov Models and Kalman Filter methods can be used for predicting a future price. We also devised a mixture predictor using HMM and KF which we called KMM. For this purpose, we hypothized HMM, KF and KMM based models that are trained on historical data can generate future data, thereby predicting this securities' price in the future. For data generation, we used Monte Carlo simulation to smooth over the irregular patterns. \Carrying the model forward in time" is achieved by a combination of Viterbi algorithm and rolling the dice on hidden state transitions, in KF case, we follow the time transition equation. Another goal of this thesis was to determine how HMM, KF and KMM methods stood in comparison to other conventional methods. We picked polynomial regression, Neural Networks (ANN) and plain \random guess" as our comparison criteria. Random guess was expected to be the lowest performer in our tests, every method mentioned should have surpassed random guess results by wide margin. We were glad to see that this was indeed the case. We used Istanbul Stock Exchange ISE-100 and Dow Jones Industrial (DJI) Index historical data as our test data batch.