Forecasting of financial time series data possessing stable distributions by employing Stochastic Differential Equations: A review

The paper acknowledges the complex behaviour of time series data, renowned for its inherent chaotic nature and inclination towards sudden, significant high jumps. To address such intricate data, the incorporation of stochastic differential equations (SDEs) with noise can be done to accurately represent the data and its inherent traits. To better comprehend the distribution sustained by the data, the paper explores the realms of stable distribution, particularly relevant for data exhibiting heavier tails. Therefore, this review highlights the utility of modelling white noise within the frame work of a non-Gaussian distribution governed by Lévy motion. In this context, it proposes using alpha stable Lévy motion due to its remarkable ability to closely mirror the data's characteristics. Thus harmonizing the noise modelling process with the data's intricate dynamics. It aims at the techniques proposed in various research papers and discerning the most effective approach for analyzing financial time series data. Additionally, it also outlines the major improvements and future implementations in this domain.