Bayesian Exponential Smooth Transition Autoregressive Model for Forecasting the Nairobi Securities Exchange 20 Share Index

The Nairobi Securities Exchange (NSE) plays a significant role in the Kenyan financial sector. The stock market indices often exhibit nonlinear characteristics which are caused by global factors, inflation trends, policy changes, investor sentiments, and external economic shocks. Traditional linear models such as Autoregressive Integrated Moving Average (ARIMA) are useful for capturing linearity overtime but are not sufficient in capturing the regime-switching dynamics of financial markets. A more realistic model is the Smooth Transition Autoregressive (STAR) models particularly the Exponential STAR (ESTAR) variant which offer a more realistic approach by modeling gradual transitions between market regimes. Despite their potential, most applications of STAR models have relied on frequentist estimation techniques leaving a gap in Bayesian approaches, particularly for ESTAR models in emerging markets like Kenya. This study has identified the regime orders of the ESTAR model for the NSE-20 share index and estimated the parameters of the ESTAR model using a Bayesian framework then obtained h-step ahead forecasts for the NSE-20 share index using the estimated ESTAR model and finally compared the forecasting performance of the Bayesian STAR model with that of the Bayesian Self-Exciting Threshold Autoregressive (SETAR) model using the NSE-20 Share Index. The analysis of simulated and real time series data from 1997 to 2026 was done in R programing software at the NSE 20 share index. Specifically, the research utilized the Bayesian approach to model uncertainty and model structure through the use of Markov Chain Monte Carlo (MCMC) methods specifically the Gibbs sampler with Metropolis-Hastings algorithm to estimate model parameters. The results of the ACF plots, trace plots and density plots showed convergence reached. The findings demonstrate that the Bayesian ESTAR model is an effective and reliable framework for modelling and forecasting the NSE-20 Share Index. By incorporating smooth regime transitions and Bayesian parameter estimation, the model provides improved predictive performance and offers a valuable tool for financial forecasting, investment analysis, and decision-making in nonlinear financial markets. This study has helped to narrow the gap between the methodologies and the empirical analysis used in modelling and forecasting financial time series in emerging markets particularly the regime switching behaviour in Kenya. It has given investors and policymakers’ strong, data-driven instruments to predict the market transitions in