Testing the stability of the functional autoregressive process

https://doi.org/10.1016/j.jmva.2008.12.008Get rights and content
Under an Elsevier user license
open archive

Abstract

The functional autoregressive process has become a useful tool in the analysis of functional time series data. It is defined by the equation Xn+1=ΨXn+εn+1, in which the observations Xn and errors εn are curves, and Ψ is an operator. To ensure meaningful inference and prediction based on this model, it is important to verify that the operator Ψ does not change with time. We propose a method for testing the constancy of Ψ against a change-point alternative which uses the functional principal component analysis. The test statistic is constructed to have a well-known asymptotic distribution, but the asymptotic justification of the procedure is very delicate. We develop a new truncation approach which together with Mensov’s inequality can be used in other problems of functional time series analysis. The estimation of the principal components introduces asymptotically non-negligible terms, which however cancel because of the special form of our test statistic (CUSUM type). The test is implemented using the R package fda, and its finite sample performance is examined by application to credit card transaction data.

AMS subject classification

62M10

Keywords

Change-point
Functional autoregressive process

Cited by (0)