Modeling stock price trends and volatility in emerging markets using ARIMA and GARCH approaches

Stock price prediction and volatility modeling are important for making financial decisions, especially in emerging markets like the Nairobi Securities Exchange (NSE). This study examines how well the Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models perform in forecasting stock prices and modeling volatility. The ARIMA (2,1,0) model was selected as the best fit using the Akaike Information Criterion (AIC), showing strong performance in capturing long-term price trends. However, an analysis of the residuals showed signs of volatility clustering, meaning ARIMA alone could not capture short-term fluctuations. To solve this, the study added a GARCH (1,1) model, which effectively captured changing volatility and improved prediction accuracy. The combined ARIMA-GARCH model reduced the Root Mean Squared Error (RMSE) from 3.1211 to 2.5786, demonstrating the value of including volatility modeling in financial time series. The results highlight the need for strong statistical models in emerging markets, where stock prices are often affected by external shocks and market inefficiencies. This research offers useful insights for investors, policymakers, and financial analysts by supporting better risk management and more accurate forecasting. Future studies could expand the model to include more stocks, macroeconomic data, and machine learning techniques to further improve results.