Modeling the Conditional Variance in the Returns on Nigeria Capital Market Variables Using Multivariate GARCH Models

Abstract

This study investigates the dynamic volatility, conditional covariance, and spillover effects between key stock market indicators in Nigeria using advanced multivariate econometric techniques. Monthly data on the All-Share Index and Market Capitalization (MC) spanning January 1996 to June 2024, comprising 1,799 observations, were obtained from the Central Bank of Nigeria and analyzed using Python-based econometric and machine learning frameworks. The return series were computed using logarithmic differencing and subjected to rigorous diagnostic procedures including descriptive statistics, normality testing, and unit root analysis. Empirical results reveal that both ASI and MC returns exhibit low mean values of 0.0093 and 0.0169 respectively, alongside high standard deviations of 0.1599 and 0.3839, indicating substantial market variability. The distributions are positively skewed (0.7037 and 0.2928) and highly leptokurtic (120.393 and 164.085), with Jarque–Bera statistics of 207,789.271 and 385,955.456 (p < 0.001), confirming strong deviations from normality and the presence of heavy tails. Unit root tests (ADF = −18.788; PP = −18.789; p < 0.001) consistently establish stationarity of the return series, validating their suitability for VAR–GARCH modelling. Time-series plots further reveal pronounced volatility clustering, structural instability, and nonlinear dependence patterns between ASI and MC returns. Three multivariate GARCH models—VECH-GARCH, BEKK- GARCH, and DCC-GARCH—were estimated and compared using forecasting performance metrics. Results indicate that VECH-GARCH performs poorly due to parameter proliferation, with the highest MSE (2.001822×1017), RMSE (4.474172×108), and MAE (2.258884×108). BEKK- GARCH improves performance with the lowest MSE (1.609398×1017) and RMSE (4.011730×108), demonstrating robustness in capturing extreme volatility shocks. However, DCC-GARCH emerges as the most efficient model overall, yielding the lowest MAE (3.120882×107), thereby providing superior average forecasting accuracy and better representation of time-varying correlations. The findings confirm strong positive conditional covariance and dynamic interdependence between stock market indicators in Nigeria. Overall, the DCC-GARCH framework offers the best balance IJASMT E- ISSN 2489-009X , between parameter efficiency, stability, and predictive accuracy for modelling volatility and risk transmission in emerging financial markets. Keyword: Modeling, Conditional, Variance, Returns, Capital, Market, Variables

References