Estimation in INAR(1) Model with Overreported Count Data

In practical applications, time series data are often affected by overreporting. To better capture these data features, this paper proposes an integer-valued process with overreporting. We discuss the bias of naive estimation that ignores overreporting and provides the corrected estimating equations. Besides, two estimation methodologies are explored that operate without requiring the error probability information. The Yule-Walker estimation is employed to estimate the parameters of the integer-valued autoregressive process under the influence of overreporting. In particular, to address the unobservability of the true process caused by spurious counts, a pseudo-maximum likelihood method based on the expectation-maximization algorithm and Gibbs sampling is presented. The asymptotic properties of the proposed estimators are studied. Simulation results demonstrate satisfactory estimation performance, and the model is further applied to a real dataset for validation.