Integer-Valued Split-BREAK Process with a General Family of Innovations and Application to Accident Count Data Modeling

• Published in: Axioms Vol. 13; no. 1; p. 40
• Main Authors: Stojanović, Vladica S., Bakouch, Hassan S., Gajtanović, Zorica, Almuhayfith, Fatimah E., Kuk, Kristijan
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-01-2024
• Subjects: Asymptotic properties; Electronic data processing; forecasting; Forest fires; Innovations; Integers; Methods; noise indicator; parameter estimation; power-series family of distributions; Random variables; Series (mathematics); simulation; Stochastic models; Stochastic processes; Time series; Traffic accidents; Serbia
• ISSN: 2075-1680; 2075-1680
• DOI: 10.3390/axioms13010040

This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution, over-dispersion and zero-inflation properties of the INSB(1) process are also examined. To estimate the unknown parameters of the INSB(1) process, an estimation procedure based on probability generating functions (PGFs) is proposed. For the obtained estimators, their asymptotic properties, as well as the appropriate simulation study, are examined. Finally, the INSB(1) process is applied in the dynamic analysis of some real-world series, namely, the numbers of serious traffic accidents in Serbia and forest fires in Greece.