Testing the goodness-of-fit of a functional autoregressive model
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916059522531328 |
|---|---|
| author | González-Manteiga, W. Ruiz-Medina, M. D. Febrero-Bande, M. |
| author_facet | González-Manteiga, W. Ruiz-Medina, M. D. Febrero-Bande, M. |
| contents | 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 \mathbb{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 \mathbb{H}, with subordinator given by the marginal probability of the involved strictly stationary Autoregressive Hilbertian process (AR\mathbb{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 Appendix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09644 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Testing the goodness-of-fit of a functional autoregressive model González-Manteiga, W. Ruiz-Medina, M. D. Febrero-Bande, M. Statistics Theory 60G10, 60G12, 60G18, 60G20, 60G22, 60G60 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 \mathbb{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 \mathbb{H}, with subordinator given by the marginal probability of the involved strictly stationary Autoregressive Hilbertian process (AR\mathbb{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 Appendix. |
| title | Testing the goodness-of-fit of a functional autoregressive model |
| topic | Statistics Theory 60G10, 60G12, 60G18, 60G20, 60G22, 60G60 |
| url | https://arxiv.org/abs/2303.09644 |