Testing the constancy of the variance for time series with a trend

Lei Jin, Li Cai and Suojin Wang

Computational Statistics & Data Analysis, 2025, vol. 208, issue C

Abstract: The assumption of constant variance is fundamental in numerous statistical procedures for time series analysis. Nonlinear time series may exhibit time-varying local conditional variance, even when they are globally homoscedastic. Two novel tests are proposed to assess the constancy of variance in time series with a possible time-varying mean trend. Unlike previous approaches, the new tests rely on Walsh transformations of squared processes after recentering the time series data. It is shown that the corresponding Walsh coefficients have desirable properties, such as asymptotic independence. Both a max-type statistic and an order selection statistic are developed, along with their asymptotic null distributions. Furthermore, the consistency of the proposed statistics under a sequence of local alternatives is established. An extensive simulation study is conducted to examine the finite-sample performance of the procedures in comparison with existing methodologies. The empirical results show that the proposed methods are more powerful in many situations while maintaining reasonable Type I error rates, especially for nonlinear time series. The proposed methods are applied to test the global homoscedasticity of a financial time series, a well log time series with a non-constant mean structure, and a vibration time series.

Keywords: Autocovariance; Bootstrap; Local alternatives; Nonlinear time series; Walsh transformation (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947325000234
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:208:y:2025:i:c:s0167947325000234

DOI: 10.1016/j.csda.2025.108147

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().