Statistical Evaluation of Nigerian Stock Exchange Returns Using GARCH Models for Volatility Estimation

Equity return volatility estimation is fundamental to investment risk management and derivative pricing on the Nigerian Stock Exchange (NGX), with GARCH-family models providing the theoretically grounded framework for capturing the time-varying volatility documented in emerging market returns. This study applies GARCH-family models to estimate and forecast volatility in Nigerian Stock Exchange All-Share Index daily returns from 2015 to 2023. The return series was tested for stationarity by ADF and KPSS tests, ARCH effects by Engle's LM test, and normality by Jarque-Bera. GARCH(1,1), EGARCH(1,1), GJR-GARCH(1,1), and APARCH(1,1) models with Student-t and generalised error distribution innovations were estimated and compared by AIC and BIC. Diagnostic tests confirmed ARCH effects (LM statistic = 42.3, p < 0.001) and significant volatility clustering. GJR-GARCH(1,1) with Student-t innovations provided the best fit (AIC = -5,812), capturing significant asymmetric volatility (leverage effect gamma = 0.14, p = 0.002), indicating that negative shocks increase subsequent volatility more than positive shocks. Volatility persistence was high (alpha + beta = 0.97). COVID-19 and 2023 election periods generated statistically significant volatility spikes. The study recommends NGX-listed investment funds adopt GJR-GARCH-based Value at Risk models and that AIICO Securities and similar operators incorporate asymmetric volatility in risk disclosure documents. Keywords: GARCH, volatility, Nigerian Stock Exchange, EGARCH, financial statistics