Long-term prediction intervals of time series

Authors:
Zhou Zhou;Zhiwei Xu;Wei Biao Wu
Affiliations:
Department of Statistics, University of Toronto, Toronto, ON, Canada;Department of Statistics, University of Chicago, Chicago, IL;Department of Computer and Information Science, University of Michigan-Dearborn, Dearborn, MI
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

We consider the problem of predicting aggregates or sums of future values of a process based on its past values. In contrast with the conventional prediction problem in which one predicts a future value given past values of the process, in our setting the number of aggregates can go to infinity with respect to the number of available observations. Consistency and Bahadur representations of the prediction estimators are established. A simulation study is carried out to assess the performance of different prediction estimators.