Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach

The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.