Aknouche, Abdelhakim and Gouveia, Sonia and Scotto, Manuel
(2023):
*Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs.*

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## 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.

Item Type: | MPRA Paper |
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Original Title: | Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs |

Language: | English |

Keywords: | integer-valued random coefficient AR, random multiplication integer-valued auto-regression, random multiplication operator, RMINAR, WLS estimators |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods |

Item ID: | 119518 |

Depositing User: | Prof. Abdelhakim Aknouche |

Date Deposited: | 30 Dec 2023 08:39 |

Last Modified: | 30 Dec 2023 08:39 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/119518 |