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Functional time series (FTS) analysis, which concerns functional data objects observed sequentially or over time, has become increasingly popular. This paper develops a change point detection method for polynomial-trend models of FTS. The proposed test statistic is based on a maximally selected CUSUM process constructed from function-valued least-squares residuals. We establish the asymptotic properties of this statistic under general stationarity and weak dependence conditions on the model innovations. Practical aspects of applying the test are discussed, and it is demonstrated in Monte-Carlo simulation experiments and an empirical analysis of electricity spot prices in Spain. This approach extends some classical polynomial-trend change point methods to functional data, and builds upon the seminal work of MacNeill (1978) and several results of Professor Marie Hušková.

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Change Point Analysis for Polynomial Trends in Functional Time Series

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  • 发表日期：

    2026年

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  • Rohit Gajendragadkar,
  • Gregory Rice

摘要

Functional time series (FTS) analysis, which concerns functional data objects observed sequentially or over time, has become increasingly popular. This paper develops a change point detection method for polynomial-trend models of FTS. The proposed test statistic is based on a maximally selected CUSUM process constructed from function-valued least-squares residuals. We establish the asymptotic properties of this statistic under general stationarity and weak dependence conditions on the model innovations. Practical aspects of applying the test are discussed, and it is demonstrated in Monte-Carlo simulation experiments and an empirical analysis of electricity spot prices in Spain. This approach extends some classical polynomial-trend change point methods to functional data, and builds upon the seminal work of MacNeill (1978) and several results of Professor Marie Hušková.