Optimal Short-Term Forecast for Locally Stationary Functional Time Series

TL;DR

This paper develops a theoretical framework for optimally predicting non-stationary functional time series with smoothly changing data mechanisms, using a novel approximation method validated on telecommunication data.

Contribution

It introduces a unified auto-regressive approximation for locally stationary functional time series and proposes a double sieve expansion method for asymptotic optimal forecasting.

Findings

Theoretical validation of the auto-regressive approximation.

Successful application to telecommunication traffic data.

Demonstration of asymptotic optimality in forecasting.

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.