Optimal Short-Term Forecast for Locally Stationary Functional Time Series

2023/07/18 by Cui, Yan, Zhou, Zhou
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2307.09148

Abstract

Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term linear prediction of non-stationary functional or curve time series with smoothly time-varying data generating mechanisms. The core of this work is to establish a unified functional auto-regressive approximation result for a general class of locally stationary functional time series. A double sieve expansion method is proposed and theoretically verified for the asymptotic optimal forecasting. A telecommunication traffic data set is used to illustrate the usefulness of the proposed theory and methodology.

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