Stock Price Prediction in India: Comparing Stochastic Differential Equations with MCMC, LSTM, and ARIMA Models and Exploring a Hybrid Approach

Abstract

The inherent volatility and nonlinearity of stock prices make them a crucial challenge in financial markets. This study investigates how well stochastic differential equations (SDEs) with parameter estimation employ the Markov Chain Monte Carlo (MCMC) algorithm to model changes in Indian stock prices. To evaluate this methods predictive accuracy we compare its performance to that of conventional Long Short-Term Memory (LSTM) networks and AutoRegressive Integrated Moving Average (ARIMA) models. A probabilistic estimation of important parameters in the SDE model is made possible by the Bayesian inference framework used in the MCMC algorithm which successfully captures market uncertainties. Our results show each models advantages and disadvantages in predicting stock prices highlighting how well-suited each is for various time horizons and market circumstances. In order to take advantage of both stochastic modeling and deep learning capabilities we also suggest a novel hybrid model that combines SDE-MCMC with LSTM and ARIMA. Results from experiments show that by fusing the advantages of machine learning and statistics the hybrid model increases forecasting accuracy. In addition to offering insights for analysts and investors in making data-driven decisions this research advances stock price prediction techniques.