Analysis and Forecasting of FTSE 100 Return Volatility Using an ARMA-GARCH Model

This paper investigates whether a relatively simple ARMA-GARCH specification is useful for modelling and forecasting daily FTSE 100 returns. Closing prices from 31 May 2023 to 28 August 2026 generate 823 percentage log returns. Of these, 758 observations are used for estimation and the final 65 trading days are kept aside as an out-of-sample test. Several low-order ARMA and GARCH specifications, under normal and Student-t errors, are compared using only the estimation sample. BIC selects ARMA(0,0) for the mean equation. For volatility, Student-t GARCH(1,1) is retained because it is parsimonious and its parameters are statistically significant. Out of sample, the mean forecast gives an RMSE of 0.5760 and an MAE of 0.4190, only slightly better than a zero-return benchmark. The reported directional accuracy of 56.9% is largely explained by the positive constant mean, which produces a positive sign forecast on every test day. For conditional variance, GARCH performs better under MAE, whereas the 20-day rolling variance has lower MSE and QLIKE. Overall, the model is more useful for tracking changes in risk than for forecasting the short-run direction of FTSE 100 returns.