Modeling Time-Varying Volatility in Nigerian Stock Returns Using a State Space Framework

This study compared a state-space stochastic-volatility model with GARCH(1,1) and EGARCH(1,1) for daily returns represented at the scale of the Nigerian Exchange All-Share Index. The constructed daily series covered 4 January 2010 to 31 December 2024 and contained 3,912 observations. Models were estimated on 3,129 observations, with 783 held out for chronological one-step-ahead forecast evaluation. The state-space specification represented log variance as a latent autoregressive process and used a Kalman filter with a Gaussian approximation to the log-squared-return observation. GARCH and EGARCH passed the reported residual checks. Among the return-density models, EGARCH had the lower in-sample AIC and GARCH the lower BIC. GARCH recorded the lowest holdout QLIKE loss (1.1071), followed by EGARCH (1.1076) and state-space SV (1.1428). EGARCH had the lowest RMSE (2.4182), while state-space SV had the lowest MAE (1.2813). Diebold-Mariano tests found higher QLIKE loss for state-space SV than for either benchmark; the GARCH-EGARCH difference was not statistically distinguishable. The QLIKE ranking was unchanged under the error-distribution robustness checks. Latent-state flexibility did not produce lower one-step-ahead QLIKE loss in this daily design.