# On model selection from a finite family of possibly misspecified time series models

@article{Hsu2019OnMS, title={On model selection from a finite family of possibly misspecified time series models}, author={Hsiang-Ling Hsu and Ching-Kang Ing and Howell Tong}, journal={The Annals of Statistics}, year={2019} }

Consider finite parametric time series models. “I have n observations and k models, which model should I choose on the basis of the data alone” is a frequently asked question in many practical situations. This poses the key problem of selecting a model from a collection of candidate models, none of which is necessarily the true data generating process (DGP). Although existing literature on model selection is vast, there is a serious lacuna in that the above problem does not seem to have…

## Tables from this paper

## 18 Citations

FROM A FINITE FAMILY OF POSSIBLY MISSPECIFIED TIME SERIES MODELS By

- Computer Science
- 2018

A misspecification-resistant information criterion (MRIC) is proposed and it is shown that MRIC can be used in conjunction with a high-dimensional model selection method to select the (asymptotically) best predictive model across several high- dimensional misspecified time series models.

On asymptotic risk of selecting models for possibly nonstationary time-series

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This paper extends the existing asymptotic risk results in threefold: a general I(d) process; a same-realization prediction; and an information criterion more general than AIC, which is arguably most suitable for univariate time series in which the lags are naturally ordered.

Efficient and Consistent Data-Driven Model Selection for Time Series

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This paper proves that consistent model selection criteria outperform classical AIC criterion in terms of efficiency and derives from a Bayesian approach the usual BIC criterion, by keeping all the second order terms of the Laplace approximation, a data-driven criterion denoted KC’.

Consistent model selection criteria and goodness-of-fit test for affine causal processes

- Mathematics, Computer Science
- 2019

This paper studies the model selection problem in a large class of causal time series models, which includes both the ARMA or AR(∞) processes, as well as the GARCH or ARCH(∞), APARCH, ARMA-GARCH and…

Large-scale model selection in misspecified generalized linear models

- Computer ScienceBiometrika
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The framework of model selection principles under the misspecified generalized linear models presented in Lv and Liu (2014) are exploited and the asymptotic expansion of the posterior model probability in the setting of high-dimensional misspecification is investigated.

Large-Scale Model Selection with Misspecification

- Computer Science, Economics
- 2018

This paper suggests the high-dimensional generalized Bayesian information criterion with prior probability (HGBIC_p) for large-scale model selection with misspecified models and characterizes the impacts of both model misspecification and high dimensionality on model selection.

A multivariate extension of the Misspecification-Resistant Information Criterion

- Mathematics, Computer Science
- 2022

This article obtains an asymptotic expression for the mean squared prediction error matrix, the vectorial MRIC and proves the consistency of its method-of-moments estimator, and shows with an example that, in presence of misspeciﬁcation, the vectorsial MR IC identiﬂes the best predictive model whereas traditional information criteria like AIC or BIC fail to achieve the task.

Strongly consistent model selection for general causal time series

- Mathematics, Computer Science
- 2020

A ug 2 02 0 Strong consistent model selection for general causal time series August 21 , 2020

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We consider the strongly consistent question for model selection in a large class of causal time series models, including AR(∞), ARCH(∞), TARCH(∞), ARMA-GARCH and many classical others processes. We…

An empirical study on the parsimony and descriptive power of TARMA models

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This work shows that the first order threshold autoregressive moving-average process, TARMA(1,1) exhibits complex, high-dimensional, behaviour with parsimony, and studies the descriptive power of the TAR MA model with respect to the class of autore progressive models, seen as universal approximators.

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