  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.
