Fourier approach to goodness-of-fit tests for Gaussian random processes

Petr Čoupek, Viktor Dolník, Zdeněk Hlávka and Daniel Hlubinka ()
Additional contact information
Petr Čoupek: Charles University
Viktor Dolník: Charles University
Zdeněk Hlávka: Charles University
Daniel Hlubinka: Charles University

Statistical Papers, 2024, vol. 65, issue 5, No 12, 2937-2972

Abstract: Abstract A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the Cramér-von Mises distance between the observed empirical characteristic functional (CF) and the theoretical CF corresponding to the null hypothesis stating that the functional observations (process paths) were generated from a specific parametric family of Gaussian processes, possibly with unknown parameters. The asymptotic null distribution of the proposed test statistic is derived also in the presence of these nuisance parameters, the consistency of the classical parametric bootstrap is established, and some particular choices of the necessary tuning parameters are discussed. The empirical level and power are investigated in a simulation study involving GoF tests of an Ornstein–Uhlenbeck process, Vašíček model, or a (fractional) Brownian motion, both with and without nuisance parameters, with suitable Gaussian and non-Gaussian alternatives.

Keywords: Functional data; Goodness-of-fit test; Characteristic functional; Gaussian processes; 62F05; 62F12; 62M07; 60E10 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-023-01510-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01510-4

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-023-01510-4

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().