A goodness-of-fit test for functional time series with applications to Ornstein-Uhlenbeck processes

J. Álvarez-Liébana, A. López-Pérez, W. González-Manteiga and M. Febrero-Bande

Computational Statistics & Data Analysis, 2025, vol. 203, issue C

Abstract: High-frequency financial data can be collected as a sequence of time-ordered curves, such as intraday prices. The Functional Data Analysis (FDA) framework offers a powerful approach to uncover information embedded in the shape of the daily paths, often unavailable from classical statistical methods. A novel goodness-of-fit test for autoregressive Hilbertian (ARH) models is introduced, imposing only the Hilbert-Schmidt condition on the autocorrelation operator. The test statistic is formulated in terms of a Cramér–von Mises norm, with calibration achieved via a wild bootstrap resampling procedure. A simulation study examines the test's finite-sample performance in terms of power and size. Furthermore, a new specification test for diffusion models, including Ornstein-Uhlenbeck processes, is proposed, illustrated with an application to intraday currency exchange rates. Specifically, a two-stage methodology is proffered: firstly, the relationship between functional samples and their lagged values is assessed using an ARH(1) model; second, under linearity, a functional F-test is conducted.

Keywords: Currency exchange rates; Diffusion models; Functional time series; Goodness-of-fit; Specification test; Ornstein-Uhlenbeck process (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:203:y:2025:i:c:s0167947324001762

DOI: 10.1016/j.csda.2024.108092

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