Power Weighted Densities for Time Series Data

TL;DR

This paper introduces Power Weighted Densities (PWD), a simple and effective method for handling non-stationarity in time series prediction by down-weighting older data, outperforming traditional models in financial applications.

Contribution

The paper proposes PWD as a novel, computationally simple alternative to state-space models for non-stationary time series analysis, unifying existing techniques like rolling window estimation.

Findings

PWD improves predictive accuracy over stationary models.

It outperforms other non-stationary methods in financial data.

The method reveals evolving market factor importance.

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.