Optimised block bootstrap: an efficient variant of circular block bootstrap method with application to South African economic time series data

This study introduced the optimized block bootstrap (OBB), a novel method designed to enhance time series prediction by reducing the number of blocks while maintaining their representativeness. OBB minimized block overlap, resulting in greater computational efficiency while preserving the temporal structure of data. The method was evaluated through extensive simulations of autoregressive moving average (ARMA) models and South Africa economic data which included inflation rates, gross domestic product (GDP) growth, interest rates, and unemployment rates. Results demonstrated that OBB consistently outperformd circular block bootstrap (CBB), providing more accurate forecasts with lower root mean square error (RMSE), which assessed variance, and lower mean absolute error (MAE), which measured bias, across various time series models and parameter settings. Consequently, the OBB method was applied to forecasting of the South Africa economic data, extending up to 2027. The novel approach presented by OBB offered a valuable tool for improving predictive accuracy in time series forecasting, with potential applications across diverse fields such as finance and environmental modeling.