Poisson-Lindley minification INAR process with application to financial data

Vladica S. Stojanović; Hassan S. Bakouch; Radica Bojičić; Gadir Alomair; Shuhrah A. Alghamdi; Vladica S. Stojanović; Hassan S. Bakouch; Radica Bojičić; Gadir Alomair; Shuhrah A. Alghamdi

doi:10.3934/math.20241102

AIMS Mathematics

2024, Volume 9, Issue 8: 22627-22654. doi: 10.3934/math.20241102

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Research article

Poisson-Lindley minification INAR process with application to financial data

1.
Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, Belgrade 11060, Serbia
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt
4.
Department of Mathematics & Informatics, Faculty of Economics, University of Kosovska Mitrovica, Kosovska Mitrovica 38220, Serbia
5.
Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
6.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia

Received: 26 March 2024 Revised: 01 July 2024 Accepted: 09 July 2024 Published: 22 July 2024
MSC : 62M10, 60G10, 62M20, 62P05

This paper introduces the Poisson-Lindley minification integer-valued autoregressive (PL-MINAR) process, a novel statistical model for analyzing count time series data. The modified negative binomial thinning and the Poisson-Lindley (PL) marginal distribution served as the foundation for the model. The proposed model was examined in terms of its basic stochastic properties, especially related to conditional stochastic measures (e.g., transition probabilities, conditional mean and variance, autocorrelation function). Through comprehensive simulations, the effectiveness of various parameter estimation techniques was validated. The PL-MINAR model's practical utility was demonstrated in analyzing the number of Bitcoin transactions and stock trades, showing its superior or comparable performance to the established INAR model. By offering a robust tool for financial time series analysis, this research holds potential for significant improvements in forecasting and understanding market dynamics.
- count time series,
- minification processes,
- forecasting,
- parameters estimation,
- simulation,
- stock and bitcoin data
Citation: Vladica S. Stojanović, Hassan S. Bakouch, Radica Bojičić, Gadir Alomair, Shuhrah A. Alghamdi. Poisson-Lindley minification INAR process with application to financial data[J]. AIMS Mathematics, 2024, 9(8): 22627-22654. doi: 10.3934/math.20241102

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Abstract

This paper introduces the Poisson-Lindley minification integer-valued autoregressive (PL-MINAR) process, a novel statistical model for analyzing count time series data. The modified negative binomial thinning and the Poisson-Lindley (PL) marginal distribution served as the foundation for the model. The proposed model was examined in terms of its basic stochastic properties, especially related to conditional stochastic measures (e.g., transition probabilities, conditional mean and variance, autocorrelation function). Through comprehensive simulations, the effectiveness of various parameter estimation techniques was validated. The PL-MINAR model's practical utility was demonstrated in analyzing the number of Bitcoin transactions and stock trades, showing its superior or comparable performance to the established INAR model. By offering a robust tool for financial time series analysis, this research holds potential for significant improvements in forecasting and understanding market dynamics.

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