Power Weighted Densities for Time Series Data

Abstract

While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the parameters of a chosen time series model. In our power-weighted density (PWD) approach, observations in the distant past are down-weighted in the likelihood function relative to more recent observations, while still giving the practitioner control over the choice of data model. One of the most popular non-stationary techniques in the academic finance community, rolling window estimation, is a special case of our PWD approach. Our PWD framework is a simpler alternative compared to popular state-space methods that explicitly model the evolution of an underlying state vector. We demonstrate the benefits of our PWD approach in terms of predictive performance compared to both stationary models and alternative non-stationary methods. In a financial application to thirty industry portfolios, our PWD method has a significantly favorable predictive performance and draws a number of substantive conclusions about the evolution of the coefficients and the importance of market factors over time.