Random multiplication versus random sum: autoregressive-like models with integer-valued random inputs

A publicar em Computational Statistics and Data Analysis
https://doi.org/10.1016/j.csda.2025.108323

A common approach to analyze time series of counts is to fit models based on random sum operators. As an alternative, this paper introduces time series models based on a random multiplication operator, which is simply the multiplication of a variable operand by an integer-valued random coefficient, whose mean is the constant operand. Such an operation is endowed into autoregressive-like models with integer-valued random inputs, addressed as RMINAR. Two special variants are studied, namely the -valued random coefficient autoregressive model and the -valued random coefficient multiplicative error model. Furthermore, -valued extensions are also considered. The dynamic structure of the proposed models is studied in detail. In particular, their corresponding solutions are everywhere strictly stationary and ergodic, which is not common in either the literature on integer-valued time series models or real-valued random coefficient autoregressive models. Therefore, RMINAR model parameters are estimated using a four-stage weighted least squares estimator, with consistency and asymptotic normality established everywhere in the parameter space. Finally, the performance of the new RMINAR models is illustrated with simulated and empirical examples.