Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics

Abstract

The manuscript proposes a novel bounded proportional autoregressive (PAR) process based on the quasi-Lindley half-logistic unit (QHU) distribution, termed the QHU-PAR(1) process. Fundamental probabilistic properties of the process are established, including its Markov structure, moments, and stationarity conditions. A pseudo-innovation-based parameter estimation procedure is performed, demonstrating strong consistency and asymptotic normality of the resulting estimators. A Monte Carlo study is also conducted, showing satisfactory performance of the proposed estimators on finite samples, while the practical utility of the model is illustrated through the analysis of normalized crime-related time series. Comparative results show that the proposed QHU-PAR(1) process outperforms some competing specifications, highlighting its flexibility and efficiency for modeling bounded and asymmetric stochastic phenomena.