Document Type : Original Article
Authors
1
Department of Applied Studies, Malawi Institute of Technology, Malawi University of Science and Technology, Limbe, Malawi
2
School of Mathematical Sciences, Department of Statistics and Actuarial Science, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana
3
School of Engineering and Technology, Department of Electronics and Computer Engineering, Soroti University, Arapai, Uganda
Abstract
Growth models play a pivotal role in diverse fields, such as population dynamics, epidemiology, finance, and ecological systems. Traditionally, deterministic growth models have been extensively employed to capture various aspects of growth phenomena. However, in real-world scenarios, stochasticity is inherent in the data, challenging the suitability of deterministic models. Consequently, there is a growing interest in developing stochastic growth models capable of accommodating inherent uncertainties. This study addresses three fundamental questions within the context of stochastic growth modeling. Firstly, it investigates the continued reliability of the Method of Three Selected Points (MTSP) for estimating parameters in stochastic differential equations (SDEs), given the increasing popularity of stochastic models over deterministic ones. Secondly, it explores the required form of SDEs that maximizes the success and reliability of the MTSP approach. Lastly, it conducts a comparative analysis of the MTSP method against commonly employed techniques in the literature.
To address these questions, we propose a novel approach to constructing SDEs that enhance the stability of both bounded and unbounded stochastic growth models. By carefully selecting the form of the diffusion coefficient, we achieve higher accuracy in estimating the parameters of the drift coefficient. Through empirical simulations and a comprehensive reliability analysis using real stock data, we demonstrate the superior performance of the MTSP method when compared to the Pseudo-maximum likelihood method and physics-informed neural networks within the framework of SDEs. Our findings underscore the continued effectiveness of the MTSP method for estimating parameters in stochastic growth models, even in an era where stochastic models dominate. Additionally, we provide insights into the optimal structure of SDEs for maximizing the reliability of the MTSP approach. Thus, the study contributes to the ongoing dialogue surrounding stochastic growth modeling and offers a robust methodology for parameter estimation in this context, with practical applications in fields ranging from epidemiology to finance.
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