# Multivariate time series models for mixed data

arXiv: https://arxiv.org/abs/2104.01067 · HTML: https://mlsanity.com/paper/2104.01067/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2021.

## Built on by (most cited first, 2 of 2)

- [How Intermodal Interaction Affects the Performance of Deep Multimodal Fusion for Mixed-Type Time Series](https://mlsanity.com/paper/2406.15098/) (2024)
- [A Transferable Autologistic Model for Predicting Rare Failures in Heterogeneous Equipment](https://mlsanity.com/paper/2608.06695/) (2026)

## Abstract (arXiv)

We introduce a general approach for modeling the dynamic of multivariate time series when the data are of mixed type (binary/count/continuous). Our method is quite flexible and 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 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.