Aishatu Kaigama1*, Harun Bakari Rann2 Yusuf Abbakar Mohammed3 Farid Zamani4 & Hamidu Aliyu
Chamalwa5
1Department of Mathematics and Computer Science, Borno State University, Nigeria
2Department of Statistics, University of Maiduguri PM.B 1069, Maiduguri Borno State Nigeria
3Department of Statistics, University of Maiduguri PM.B 1069, Maiduguri Borno State Nigeria
4School of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia (UPM), 43400 Serdangi, Selangor, Darul Ehsan, Malaysia.
5Department of Statistics, University of Maiduguri PM.B 1069, Maiduguri Borno State Nigeria
*Corresponding author’s Email: a.kaigama@yahoo.com, doi.org/10.55639/607.02010043
ABSTRACT
This study introduces the Cosine Exponentiated Generalized Student’s t (CEGST) distribution as a novel error innovation for GARCH-type models to better capture financial market volatility. It evaluates GARCH(1,1), GARCH(1,2), and GARCH(2,1) models using simulated data and daily returns from the Nigerian Stock Exchange between 7 February 2012 and 28 November 2023 making a total of 2,948 observations. Models were estimated in R using the ‘fgarch’ package and the performance was assessed via AIC, BIC, MAE, MSE and RMSE. Simulation results show the GARCH(1,2) CEGST model (Case 1) achieved the best performance with lowest values across all criteria: AIC (–1360.182), BIC (–1389.629), MAE (0.09461), MSE (0.01652), RMSE (0.12853), indicating improved fit through an additional GARCH lag. In contrast, empirical results on NSE data favored the GARCH(2,1) CEGST model, achieving superior in-sample performance with AIC (–46,717.62), BIC (–46,663.72), MAE (0.00636), MSE (9.31 × 10⁻⁵) and RMSE (0.00965). Residual diagnostics revealed no serial correlation or ARCH effects at the 5% level. The CEGST-based GARCH models effectively capture key features of volatility in emerging markets such as cyclical behavior, heavy tails and market shocks. The findings demonstrate the efficacy of the CEGST distribution in portraying the complex volatility patterns typical of developing financial markets.
Keywords:
GARCH model,
CEGST
Distribution,
Volatility
Modeling,
Nigeria Stock