Density Forecasting Using Hidden Markov Experts

We present a framework for predicting the conditional distributions of future observations that is well suited for skewed, fat-tailed, and multi-modal time series. This framework allows to address questions about the nature of an observed time series, such as: Are there discrete subprocesses underlying the observed data? If so, do they exhibit a hidden Markov structure, or are they better described by using external variables? Are the sub-processes nonlinear? The answers to these questions are obtained by building predictive models on part of the available data, and evaluating these models on held-out data using several methods that capture both quantitative and qualitative aspects of the predicted densities. Speci cally, we discuss the similarities and di erences between two architectures, gated experts and hidden Markov experts. For the task of predicting the daily distributions of S&P500 returns, the hidden Markov assumption leads to better density forecasts than gated experts. Both architectures are contrasted to a simple superposition of forecasts. Applications of good density forecasts range from building trading models to computing risk measures that capture non-Gaussian tails.