Testing the stability of the functional autoregressive process
The functional autoregressive process has become a useful tool in the analysis of functional time series data. It is defined by the equation , in which the observations Xn and errors [epsilon]n are curves, and is an operator. To ensure meaningful inference and prediction based on this model, it is important to verify that the operator does not change with time. We propose a method for testing the constancy of 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.
Year of publication: |
2010
|
---|---|
Authors: | Horváth, Lajos ; Husková, Marie ; Kokoszka, Piotr |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 101.2010, 2, p. 352-367
|
Publisher: |
Elsevier |
Subject: | 62M10 Change-point Functional autoregressive process |
Saved in:
Saved in favorites
Similar items by person
-
Change-point monitoring in linear models
Aue, Alexander, (2006)
-
ESTIMATORS AND TESTS FOR CHANGE IN VARIANCES
Gombay, Edit, (1996)
-
Tests of Normality of Functional Data
Górecki, Tomasz, (2020)
- More ...