Journal of Multivariate Analysis· 2026Q1
Testing the goodness-of-fit of a functional autoregressive model
- 1citations
- Q1SCImago
- 2026year
Short summary
A new goodness-of-fit test for functional time series linear autocorrelation models is introduced, based on an empirical process that converges to a time-changed Wiener process in a Hilbert space.
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Key points
- Introduces a new goodness-of-fit (GoF) test for functional time series linear autocorrelation models.
- The test is based on an empirical process with residuals and covariate index sets in a separable Hilbert space H.
- A functional central limit theorem shows convergence to a time-changed Wiener process in H.
- The large sample behavior and consistency of the test are analyzed under simple and composite null hypotheses.
AI-generated from the title and abstract; the full text is not read.
Abstract
The proposed Goodness–of–Fit (GoF) test for checking the linear autocorrelation model in a functional time series is based on an empirical process, whose residual marks and covariate index set are in a separable Hilbert space H . A functional central limit theorem is derived providing the convergence of the empirical process to a time–changed Wiener process evaluated in a separable Hilbert space H , with subordinator given by the marginal probability of the involved strictly stationary Autoregressive Hilbertian process (AR H (1) process). The large sample behavior of the test statistics is obtained under simple and composite null hypotheses. The consistency of the test is addressed under simple null hypothesis. The finite–sample performance of the testing procedure, under different families of alternatives, and random projection schemes, is illustrated in the Supplementary Material.
The authors' abstract, as published at the source. Journal of Multivariate Analysis, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics