Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates

Abstract

In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distributions and unlike the classical autoregressive framework, the conditional mean of the process also depends on some exogenous covariates. We derive a robust inference procedure based on the minimum density power divergence. Under certain regularity conditions, we establish that the proposed estimator is consistent and asymptotically normal. In the case where the conditional distribution belongs to the exponential family, we provide sufficient conditions for the existence of a stationary and ergodic $\tau $-weakly dependent solution. Simulation experiments are conducted to illustrate the empirical performances of the estimator. An application to the number of transactions per minute for the stock Ericsson B is also provided.

Keywords

Robust estimation / Minimum density power divergence / Integer-valued time series models / Exogenous covariates / 62M10 / 62F12 / 62F35

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School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature