Bayesian Predictive Synthesis
Bayesian predictive synthesis defines a coherent theoretical basis for combining multiple forecast densities, whether from models, individuals, or other sources, and extends existing forecast pooling and Bayesian model mixing methods.
Recent research at the interfaces of applied/empirical macroeconomics and Bayesian methodology development reflects renewed interest in questions of model and forecast comparison, calibration, and combination. From a Bayesian perspective, formal model uncertainty and mixing analysis is “optimal” when a closed set of models generate forecast densities; in practice, it suffers from several limitations.
Motivated by an interest in the question of foundational underpinnings of some of the specific algorithmic/empirical models for forecast density combination recently introduced, we developed a new framework called Bayesian predictive synthesis (BPS). The framework provides interpretation of traditional and recently introduced pooling methods as special cases. More importantly from a practical time series forecasting perspective, development of BPS for sequential forecasting of time series enables the use of flexible, adaptive Bayesian dynamic models that are able to respond to changes in characteristics of sets of models and forecasters over time. BPS has the potential to define fully Bayesian, interpretable models that can adapt to time-varying biases and mis-calibration of multiple models or forecasters, and generate useful insights into patterns of relationships and dependencies among them while also improving forecast accuracy.
Stochastic Volatility and Particle Learning
The estimation, inference, and prediction of volatility is one of the most crucial aspects in analyzing data with variability in order to make informed decisions. In the field of finance and economics, volatility of financial assets has been investigated with great scrutiny to further the understanding of the mechanics and structure of price movement.
One aspect of volatility that has gathered special interest is the correlation between an asset’s return and its volatility; coined the leverage effect. It is often claimed that this correlation is negative, implying that a negative (positive) shock to an asset’s return results in an increase (decrease) in its volatility. This phenomenon is intuitive, as we can expect– and often observe– that an asset under distress exhibits more variability and uncertainty compared to an asset that is stable or increasing in price. However, contrary to consensus, the lack of empirical evidence of the effect from individual stocks is paradoxical; with most stocks exhibiting zero or very weak correlation between asset returns and volatility.
To solve this paradox, we extend the SV model to include a generalized leverage function to examine the nonlinear dynamics of the correlation between an asset’s return and its volatility. To achieve this, we develop an effective Bayesian computation method using sequential Monte Carlo (SMC) by extending the particle learning method, enabling estimation of the parameters of interest in a fast, efficient, and on-line manner.
Collaboration with Teruo Nakatsuma (Keio), Asahi Ushio (Keio).
Bayesian Time Series Modelling in Marketing
© Kenichiro McAlinn, 2016.