Forecasting Distributions with Experts Advice

Abstract

This paper considers forecasts of the distribution of data whose distribution function is possibly time varying. The forecast is achieved via time varying combinations of experts’ forecasts. We derive theoretical worse case bounds for general algorithms based on multiplicative updates of the combination weights. The bounds are useful to study the properties of forecast combinations when data are nonstationary and there is no unique best model. An application with an empirical study is used to highlight the results in practice.