Univariate integer-valued time series models, including integer-valued
autoregressive (INAR) models and integer-valued generalized autoregressive condi-
tional heteroscedastic (INGARCH) models, have been well studied in the literature, but
there is little progress in multivariate models. Although some multivariate INAR mod-
els were proposed, they do not provide enough flexibility in modeling count data, such
as volatility of numbers of stock transactions. Then, a bivariate Poisson INGARCH
model was suggested by Liu (Some models for time series of counts, Disserta-
tions, Columbia University, 2012), but it can only deal with positive cross-correlation
between two components. To remedy this defect, we propose a new bivariate Pois-
son INGARCH model, which is more flexible and allows for positive or negative
cross-correlation. Stationarity and ergodicity of the new process are established. The
maximum likelihood method is used to estimate the unknown parameters, and consis-
tency and asymptotic normality for estimators are given. A simulation study is given
to evaluate the estimators for parameters of interest. Real and artificial data examples
are illustrated to demonstrate good performances of the proposed model relative to
the existing model.

EB00000004097K

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• A new bivariate integer-valued GARCH model allowing for negative cross-correlation