12 videos

14 videos

1 videos

28 videos

## Not Only Scalar Curvature Seminar

00:00:00 / 00:00:00

## Consistent model selection criteria and goodness-of-fit test for common time series models

We study the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. To tackle this issue, we consider a penalized contrast based on the quasi-likelihood of the model. We provide sufficient conditions for the penalty term to ensure the consistency of the proposed procedure as well as the consistency and the asymptotic normality of the quasi-maximum likelihood estimator of the chosen model. We also propose a tool for diagnosing the goodness-of-fit of the chosen model based on a Portmanteau test. Monte-Carlo experiments and numerical applications on illustrative examples are performed to highlight the obtained asymptotic results. Moreover, using a data-driven choice of the penalty, they show the practical efficiency of this new model selection procedure and Portemanteau test.

### Citation data

• DOI 10.24350/CIRM.V.19640303
• Cite this video Bardet Jean-Marc (6/2/20). Consistent model selection criteria and goodness-of-fit test for common time series models. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19640303
• URL https://dx.doi.org/10.24350/CIRM.V.19640303

### Bibliography

• BARDET, Jean-Marc, KAMILA, Kare, KENGNE, William, et al. Consistent model selection criteria and goodness-of-fit test for common time series models. Electronic Journal of Statistics, 2020, vol. 14, no 1, p. 2009-2052. - http://dx.doi.org/10.1214/20-EJS1709
• BARDET, Jean-Marc, WINTENBERGER, Olivier, et al. Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes. The Annals of Statistics, 2009, vol. 37, no 5B, p. 2730-2759. - http://dx.doi.org/10.1214/08-AOS674
• DOUKHAN, Paul et WINTENBERGER, Olivier. Weakly dependent chains with infinite memory. Stochastic Processes and their Applications, 2008, vol. 118, no 11, p. 1997-2013. - https://doi.org/10.1016/j.spa.2007.12.004
• FRANCQ, Christian et ZAKOIAN, Jean-Michel. GARCH models: structure, statistical inference and financial applications. John Wiley & Sons, 2010. - http://dx.doi.org/10.1002/9780470670057
• HSU, Hsiang-Ling, ING, Ching-Kang, TONG, Howell, et al. On model selection from a finite family of possibly misspecified time series models. The Annals of Statistics, 2019, vol. 47, no 2, p. 1061-1087. - http://dx.doi.org/10.1214/18-AOS1706
• LI, Wai Keung et MAK, T. K. On the squared residual autocorrelations in non‐linear time series with conditional heteroskedasticity. Journal of Time Series Analysis, 1994, vol. 15, no 6, p. 627-636. - https://doi.org/10.1111/j.1467-9892.1994.tb00217.x
• SIN, Chor-Yiu et WHITE, Halbert. Information criteria for selecting possibly misspecified parametric models. Journal of Econometrics, 1996, vol. 71, no 1-2, p. 207-225. - https://doi.org/10.1016/0304-4076(94)01701-8
• STRAUMANN, Daniel. Estimation in Conditionally Heteroscedastic Time Series Models. Lectures notes in Statistics 181. 2005. - http://dx.doi.org/10.1007/b138400

### Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

## Register

• Bookmark videos
• Add videos to see later &