Forecasting under model uncertainty: Non-homogeneous hidden Markov models with Pòlya-Gamma data augmentation

We consider finite state-space non-homogeneous hidden Markov models for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state-dependent coefficients and time-varying transition probabilities that depend on the predictors via a logistic/multinomial function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. In this paper, we aim to address this problem utilizing the recently proposed Pólya-Gamma latent variable scheme. Also, we allow for model uncertainty regarding the predictors that affect the series both linearly — in the mean — and non-linearly — in the transition matrix. Predictor selection and inference on the model parameters are based on an automatic Markov chain Monte Carlo scheme with reversible jump steps. Hence the proposed methodology can be used as a black box for predicting time series. Using simulation experiments, we illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability. An empirical study on realized volatility data shows that our methodology gives improved forecasts compared to benchmark models.     

On the directional predictability of equity premium using machine learning techniques

This paper applies a plethora of machine learning techniques to forecast the direction of the US equity premium. Our techniques include benchmark binary probit models, classification and regression trees, along with penalized binary probit models. Our empirical analysis reveals that the sophisticated machine learning techniques significantly outperformed the benchmark binary probit forecasting models, both statistically and economically. Overall, the discriminant analysis classifiers are ranked first among all the models tested. Specifically, the high-dimensional discriminant analysis classifier ranks first in terms of statistical performance, while the quadratic discriminant analysis classifier ranks first in economic performance. The penalized likelihood binary probit models (least absolute shrinkage and selection operator, ridge, elastic net) also outperformed the benchmark binary probit models, providing significant alternatives to portfolio managers.     

A Quantile Regression Approach to Equity Premium Prediction

We propose a quantile regression approach to equity premium forecasting. Robust point forecasts are generated from a set of quantile forecasts using both fixed and time‐varying weighting schemes, thereby exploiting the entire distributional information associated with each predictor. Further gains are achieved by incorporating the forecast combination methodology into our quantile regression setting. Our approach using a time‐varying weighting scheme delivers statistically and economically significant out‐of‐sample forecasts relative to both the historical average benchmark and the combined predictive mean regression modeling approach. Copyright © 2014 John Wiley & Sons, Ltd.