Gery Andrés Díaz Rubio, Simone Giannerini, Greta Goracci
arXiv 18 Feb 2022 · Mathematics — Statistics Theory
arXiv:2202.09225 · PDF · DOI · OpenAlex · Extracted main text
The Misspecification-Resistant Information Criterion (MRIC) proposed in [H.-L. Hsu, C.-K. Ing, H. Tong: On model selection from a finite family of possibly misspecified time series models. The Annals of Statistics. 47 (2), 1061--1087 (2019)] is a model selection criterion for univariate parametric time series that enjoys both the property of consistency and asymptotic efficiency. In this article we extend the MRIC to the case where the response is a multivariate time series and the predictor is univariate. The extension requires novel derivations based upon random matrix theory. We obtain an asymptotic expression for the mean squared prediction error matrix, the vectorial MRIC and prove the consistency of its method-of-moments estimator. Moreover, we prove its asymptotic efficiency. Finally, we show with an example that, in presence of misspecification, the vectorial MRIC identifies the best predictive model whereas traditional information criteria like AIC or BIC fail to achieve the task.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hsiang-Ling Hsu, Ching-Kang Ing, and Howell Tong (2019) On model selection from a finite family of possibly misspecified time series models | 0.965 | 10 | 4 | 90% |
| 2 | H. Akaike (1971) Information theory and an extension of the maximum likelihood principle | 0.511 | 2 | 1 | 100% |
| 3 | Hirotugu Akaike (1974) A new look at the statistical model identification | 0.405 | 1 | 1 | 100% |
| 4 | W. Bessler, A. Leonhardt, and D. Wolff (2016) Analyzing hedging strategies for fixed income portfolios: A bayesian approach for model selection | 0.405 | 1 | 1 | 100% |
| 5 | Roger A. Horn and Charles R. Johnson (2013) Matrix analysis | 0.405 | 1 | 1 | 100% |
| 6 | Jiming Jiang (2010) Large sample techniques for statistics | 0.405 | 1 | 1 | 100% |
| 7 | Ker-Chau Li (1987) Asymptotic optimality for $C_p$, $C_L$, cross-validation and generalized cross-validation: discrete index set | 0.405 | 1 | 1 | 100% |
| 8 | Helmut Lütkepohl (2005) New introduction to multiple time series analysis | 0.405 | 1 | 1 | 100% |
| 9 | J. Tinsley Oden and Leszek F. Demkowicz (2018) Applied functional analysis | 0.405 | 1 | 1 | 100% |
| 10 | Gregory C. Reinsel (1993) Elements of multivariate time series analysis | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 19 scored citations.