Mohamed Saidane

Learning and inference in mixed-state conditionally heteroskedastic factor models using viterbi approximation

In this paper we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co-movement among conditionally heteroskedastic financial returns and switching between different unobservable regimes. By combining conditionally heteroskedastic factor models with hidden Markov chain models (HMM), we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroskedastic financial time series. The EM algorithm that we have developed for the maximum likelihood estimation, is based on a Viterbi approximation which yields inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with a dataset on weekly average returns of closing spot prices for eight European currencies show promising results.

Contributions to the Estimation of Mixed-State Conditionally Heteroscedastic Latent Factor Models: A Comparative Study

Mixed-State conditionally heteroscedastic latent factor models attempt to describe a complex nonlinear dynamic system with a succession of linear latent factor models indexed by a switching variable. Unfortunately, despite the frameworks simplicity exact state and parameter estimation are still intractable because of the interdependency across the latent factor volatility processes. Recently, a broad class of learning and inference algorithms for time series models have been successfully cast in the framework of dynamic Bayesian networks (DBN). This paper describes a novel DBN-based switching conditionally heteroscedastic latent factor model. The key methodological contribution of this paper is the novel use of the Generalized Pseudo-Bayesian method GPB2, a structured variational learning approach and an approximated version of the Viterbi algorithm in conjunction with the EM algorithm for overcoming the intractability of exact inference in mixed-state latent factor model. The conditional EM algorithm that we have developed for the maximum likelihood estimation is based on an extended switching Kalman filter approach which yields inferences about the unobservable path of the common factors and their variances, and the latent variable of the state process. Extensive Monte Carlo simulations show promising results for tracking, interpolation, synthesis, and classification using learned models.

Improved Nonlinear Multivariate Financial Time Series Prediction with Mixed-State Latent Factor Models

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 mixed-state latent factor model (MSFM) and discuss the practical details of training such models with a new approximated version of the Viterbi algorithm in conjunction with the expectation-maximization (EM) algorithm to iteratively estimate the model parameters in a maximum-likelihood sense. The performance of the MSFM 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.

An EM-Based Viterbi Approximation Algorithm for Mixed-State Latent Factor Models

In this article, a state-space model based on an underlying hidden Markov chain model (HMM) with factor analysis observation process is introduced. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a conditionally heteroscedastic factor analysis observation process. More specifically, we concentrate on situations where the factor variances are modeled by univariate Generalized Quadratic Autoregressive Conditionally Heteroscedastic processes (GQARCH). An expectation maximization (EM) algorithm combined with a mixed-state version of the Viterbi algorithm is derived for maximum likelihood estimation. The various regimes, common factors, and their volatilities are supposed unobservable and the inference must be carried out from the observable process. Extensive Monte Carlo simulations show promising results of the algorithms, especially for segmentation and tracking tasks.