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In this article, we study a robust estimation method for a general class ofinteger-valued time series models.  The conditional distribution of the process belongs to a broad class ofdistribution and unlike classical autoregressive framework, the conditionalmean of the process also depends on some multivariate exogenous covariate.  We derive a robust inference procedure based on the minimum density powerdivergence.  Under certain regularity conditions, we establish that the proposed estimatoris consistent and asymptotically normal.  Simulation experiments are conducted to illustrate the empirical performancesof the estimator. An application to the number of transactions per minute forthe stock Ericsson B is also provided.

Density power divergence for general integer-valued time series with multivariate exogenous covariate