February 2023 Multivariate time series models for mixed data
Zinsou-Max Debaly, Lionel Truquet
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Bernoulli 29(1): 669-695 (February 2023). DOI: 10.3150/22-BEJ1474

Abstract

We introduce a general approach which unifies some previous attempts for modeling the dynamic of multivariate time series or for regression analysis when the data are of mixed type (binary/count/continuous). Our approach is quite flexible since conditionally on past values, each coordinate at time t can have a distribution compatible with a standard univariate time series model such as GARCH, ARMA, INGARCH or logistic models whereas past values of the other coordinates play the role of exogenous covariates in the dynamic. The simultaneous dependence in the multivariate time series can be modeled with a copula. Additional exogenous covariates are also allowed in the dynamic. We first study some usual stability properties of these models and then show that autoregressive parameters can be consistently estimated equation-by-equation using a pseudo-maximum likelihood method, leading to a fast implementation even when the number of time series is large. Moreover, we prove consistency results when a parametric copula model is fitted to the time series and in the case of Gaussian copulas, we show that the likelihood estimator of the correlation matrix is strongly consistent. We carefully check all our assumptions for two prototypical examples: a GARCH/INGARCH model and logistic/log-linear INGARCH model. Our results are illustrated with numerical experiments as well as two real data sets.

Citation

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Zinsou-Max Debaly. Lionel Truquet. "Multivariate time series models for mixed data." Bernoulli 29 (1) 669 - 695, February 2023. https://doi.org/10.3150/22-BEJ1474

Information

Received: 1 April 2021; Published: February 2023
First available in Project Euclid: 13 October 2022

MathSciNet: MR4497263
zbMATH: 07634408
Digital Object Identifier: 10.3150/22-BEJ1474

Keywords: mixed data , observation-driven models , time series

Vol.29 • No. 1 • February 2023
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