Optimal Prediction with Conditionally Heteroskedastic Factor Analysed Hidden Markov Models

摘要

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear conditionally heteroskedastic latent factor model in a hybrid conditionally heteroskedastic factor analysed hidden Markov model (CHFAHMM) and discuss the practical details of training such models with a new approximated version of the Viterbi algorithm in conjunction with the expectation-maximization algorithm to iteratively estimate the model parameters in a maximum-likelihood sense. The performance of the CHFAHMM is evaluated on both simulated and financial data sets. On the basis of out-of-sample forecast encompassing tests as well as other measures for forecasting accuracy, our results indicate that the use of this new method yields overall better forecasts than those generated by competing models.