In this paper, we consider the problem of testing for a parameter change
in bivariate Poisson integer-valued GARCH(1, 1) models, constructed via a trivariate
reduction method of independent Poisson variables. We verify that the conditional
maximum-likelihood estimator of the model parameters is asymptotically normal.
Then, based on these results, we construct CMLE- and residual-based CUSUM tests
and derive that their limiting null distributions are a function of independent Brownian
bridges. A simulation study and real data analysis are conducted for illustration.

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• Asymptotic normality and parameter change test for bivariate Poisson INGARCH models