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Empirical spectral processes for stationary state space models
Multi angle
Authors : Fasen-Hartmann, Vicky (Author of the conference)
CIRM (Publisher )
62F03 - Hypothesis testing
62F12 - Asymptotic properties of estimators
62M10 - Time series, auto-correlation, regression, etc.
CIRM (Publisher )
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Abstract :
In this talk, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling distance is fixed and the driving Lévy process has at least a finite fourth moment. Under different assumptions on the function space and the moments of the driving Lévy process we derive a central limit theorem for the function-indexed normalized weighted integrated periodogram. Either the assumption on the function space or the assumption on the existence of moments of the Lévy process is weaker. The results can be used to derive the asymptotic behavior of the Whittle estimator and to construct goodness-of-fit test statistics as the Grenander-Rosenblatt statistic and the Cramér-von Mises statistic.
Keywords : Cramér-von mises test; empirical spectral process; functional central limit theorem; good- ness of fit test; Grenander-Rosenblatt test; MCARMA process; periodogram, state space model
MSC Codes : Keywords : Cramér-von mises test; empirical spectral process; functional central limit theorem; good- ness of fit test; Grenander-Rosenblatt test; MCARMA process; periodogram, state space model
62F03 - Hypothesis testing
62F12 - Asymptotic properties of estimators
62M10 - Time series, auto-correlation, regression, etc.
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 25/07/2022 Conference Date : 04/07/2022 Subseries : Research talks arXiv category : Statistics Theory Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:40:10 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-07-04-Faesen.mp4 
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Information on the Event
Event Title : Heavy Tails, Long-Range Dependence, and Beyond / Queues lourdes, dépendance de long terme et au-delàEvent Organizers : Biermé, Hermine ; Kulik, Rafal ; Mikosch, Thomas ; Wang, Yizao ; Wintenberger, Olivier Dates : 04/07/2022 - 08/07/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2633.html
Citation Data
DOI : 10.24350/CIRM.V.19937703Cite this video as: Fasen-Hartmann, Vicky (2022). Empirical spectral processes for stationary state space models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19937703 URI : http://dx.doi.org/10.24350/CIRM.V.19937703 |
See Also
- [Multi angle] Function valued random fields: tangents, intrinsic stationarity, self-similarity / Author of the conference Stoev, Stilian.
- [Multi angle] Power-laws and weak convergence of the Kingman coalescent / Author of the conference Hult, Henrik.
- [Multi angle] Branching random walk with innite progeny mean / Author of the conference Hazra, Rajat Subhra.
Bibliography
- FASEN-HARTMANN, Vicky et MAYER, Celeste. Empirical spectral processes for stationary state space processes. arXiv preprint arXiv:2202.12589, 2022. - https://doi.org/10.48550/arXiv.2202.12589
- BARDET, Jean‐Marc, DOUKHAN, Paul, et LEÓN, José Rafael. Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate. Journal of Time Series Analysis, 2008, vol. 29, no 5, p. 906-945. - https://doi.org/10.1111/j.1467-9892.2008.00588.x
- DAHLHAUS, Rainer. Empirical spectral processes and their applications to time series analysis. Stochastic Processes and their Applications, 1988, vol. 30, no 1, p. 69-83. - https://doi.org/10.1016/0304-4149(88)90076-2
- DAHLHAUS, Rainer et POLONIK, Wolfgang. Empirical spectral processes for locally stationary time series. Bernoulli, 2009, vol. 15, no 1, p. 1-39. - http://dx.doi.org/10.3150/08-BEJ137
- MIKOSCH, Thomas et NORVAIŠA, Rimas. Uniform convergence of the empirical spectral distribution function. Stochastic processes and their applications, 1997, vol. 70, no 1, p. 85-114. - https://doi.org/10.1016/S0304-4149(97)00053-7
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