This study investigates the forecasting accuracy of stock prices and indices in two developed countries, the UK and the US, and two developing countries, China and India, covering a range of market capitalisations, spanning large-, mid-, and small-cap companies and indices. This study is based on data collected over a period of 13 years. I deploy Particle-Swarm-Optimised Radial Basis Function Neural Networks (i.e., PSO-RBFNNs) and compare their performance with that of the traditional RBF Neural Network (i.e., RBFNN) model and two benchmark econometric models: the ARIMA model and the Holt–Winters model. This study employs technical indicators. The results show that in developed countries, econometrics models often perform better than neural network models, except for the US small-cap stock index S&P 600, while the PSO-RBFNN model outperforms the traditional RBFNN model in the vast majority of cases due to the optimisation of the parameters of the RBFNN model by the particle swarm optimisation algorithm. In emerging market data, neural network models outperform econometric models, while PSO-RBF performs better than or similarly to RBF in the vast majority of cases. As observed from the results, neural networks are able to provide better predictive performance for data containing complex nonlinear patterns and relationships to some extent.