A beta prime ARMA model for positive time series

Aknouche, Abdelhakim and Almohaimeed, Bader and Dimitrakopoulos, Stefanos (2025): A beta prime ARMA model for positive time series.

Abstract

A class of generalized ARMA models with an identity link function and a conditional beta prime (BP-ARMA) distribution is proposed for modeling positive time series. Sufficient and necessary conditions for the existence of an ergodic stationary BP-ARMA process having finite moments are first proposed. Then, the parameters are estimated using the geometric quasi-maximum likelihood method, the convergence and asymptotic normality of which are shown under reasonable assumptions. The proposed methodology is illustrated through a simulation study and an application to the S&P 500 volume.

• Item Type: MPRA Paper
• Language: English
• Keywords: Nonnegative time series data, Beta Prime ARMA, Generalized ARMA, ergodicity, Two-stage weighted least squares, Geometric QMLE.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C41 - Duration Analysis ; Optimal Timing Strategies

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