RT Journal Article
T1 A goodness-of-fit test for functional time series with applications to Ornstein-Uhlenbeck processes
A1 Álvarez-Liébana, Javier
A1 López Pérez, Alejandra
A1 González Manteiga, Wenceslao
A1 Febrero Bande, Manuel
K1 Currency exchange rates
K1 Diffusion models
K1 Functional time series
K1 Goodness-of-fit
K1 Ornstein-Uhlenbeck process
K1 Specification test
AB 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.
PB Elsevier
YR 2024
FD 2024
LK https://hdl.handle.net/10347/46494
UL https://hdl.handle.net/10347/46494
LA eng
NO Álvarez-Liébana, López-Pérez, González-Manteiga, & Febrero-Bande. (2025). A goodness-of-fit test for functional time series with applications to Ornstein-Uhlenbeck processes. Computational Statistics and Data Analysis, 203. https://doi.org/10.1016/J.CSDA.2024.108092
NO The authors gratefully thank Spanish National Research Council for the computing resources of the Supercomputing Center of Galicia (CESGA), and full professor M. D. Ruiz-Medina (University of Granada) for her suggestions. The first author acknowledges support from grants PID2020-116587GB-I00 and PGC2018-099549-B-I00, from the Spanish Ministry of Economy and Competitiveness. The second, third and fourth authors acknowledge financial support from grant PID2020-116587GB-I00 also from the same agency.
DS Minerva
RD 6 jun 2026