Power-weighted densities for time series data. (English) Zbl 1359.62393

McCarthy, Daniel; Jensen, Shane T.

Ann. Appl. Stat. 10, No. 1, 305-334 (2016).

Summary: While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by nonstationarity. We develop a fast and effective approach to allow for nonstationarity 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 nonstationary 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 nonstationary 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.

MSC:

62M20	Inference from stochastic processes and prediction
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

time series analysis; power prior; forecasting; finance

Software:

BayesDA; dlm

References:

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