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

Abdelhakim Aknouche, Sonia Gouveia and Manuel Scotto

MPRA Paper from University Library of Munich, Germany

Abstract: A common approach to analyze count time series 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 operation is endowed into auto-regressive-like models with integer-valued random inputs, addressed as RMINAR. Two special variants are studied, namely the N-valued random coefficient auto-regressive model and the N-valued random coefficient multiplicative error model. Furthermore, Z-valued extensions are considered. The dynamic structure of the proposed models is studied in detail. In particular, their corresponding solutions are everywhere strictly stationary and ergodic, a fact that is not common neither in the literature on integer-valued time series models nor real-valued random coefficient auto-regressive models. Therefore, the parameters of the RMINAR model are estimated using a four-stage weighted least squares estimator, with consistency and asymptotic normality established everywhere in the parameter space. Finally, the new RMINAR models are illustrated with some simulated and empirical examples.

Keywords: integer-valued random coefficient AR; random multiplication integer-valued auto-regression; random multiplication operator; RMINAR; WLS estimators (search for similar items in EconPapers)
JEL-codes: C13 C22 C25 C43 C51 C53 (search for similar items in EconPapers)
Date: 2023-12-18, Revised 2023-12-18
New Economics Papers: this item is included in nep-dcm, nep-ecm and nep-ets
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