First-order multivariate integer-valued autoregressive model with multivariate mixture distributions

Abstract

The univariate integer-valued time series has been extensively studied, but literature on multivariate integer-valued time series models is quite limited and the complex correlation structure among the multivariate integer-valued time series is barely discussed. In this study, we proposed a first-order multivariate integer-valued autoregressive model to characterize the correlation among multivariate integer-valued time series with higher flexibility. Under the general conditions, we established the stationarity and ergodicity of the proposed model. With the proposed method, we discussed the models with multivariate Poisson-lognormal distribution and multivariate geometric-logitnormal distribution and the corresponding properties. The estimation method based on EM algorithm was developed for the model parameters and extensive simulation studies were performed to evaluate the effectiveness of proposed estimation method. Finally, a real crime dataset was analysed to demonstrate the advantage of the proposed model with comparison to the other models.

Keywords:

• EM algorithm
• multivariate Poisson-lognormal distribution
• multivariate geometric-logitnormal distribution
• thinning operator

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 51578471] and the Fundamental Research Funds for the Central Universities [grant number 2682021ZTPY078].