Taking time seriously: hidden Markov experts applied to financial engineering

Abstract

Most traditional time series models are global models based on local time information: they assume that the state can be fully and locally (in time) characterized with a finite embedding space. Prediction then amounts to simple regression. Unfortunately, there are many situations in which simple regression is not sufficient to model the temporal structure in a time series. The authors introduce an architecture that they call hidden Markov experts. It is based on hidden Markov models used in speech recognition research. By introducing the concept of hidden states, hidden Markov experts model time dependency of time series explicitly as a first-order Markov model with transitions between these hidden states. Within each state, local models are applied to estimate the probability density, which can be linear or nonlinear depending on the situation. The paper first discusses the statistical framework and the learning algorithm of hidden Markov experts, then applies them to daily S&P500 data and to high frequency currency exchange rate data. The hidden Markov experts have better profit than the linear and nonlinear global models. The volatilities of the time series can be characterized by the hidden states.

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