MODELLING RETURN UNPREDICTABILITY WITH THE ODD GENERALIZED EXPONENTIAL LAPLACE DISTRIBUTION: A SIMULATION STUDY

R. O David; A. I Ishaq; C. N Nnamani; A. A Umar; Y Zakari; J. Obalowu

R. O David Department of Statistics, Ahmadu Bello University, Zaria
A. I Ishaq Department of Statistics, Ahmadu Bello University, Zaria
C. N Nnamani Department of Statistics, Ahmadu Bello University, Zaria
A. A Umar Department of Statistics, Ahmadu Bello University, Zaria
Y Zakari Department of Statistics, Ahmadu Bello University, Zaria
J. Obalowu Department of Statistics, University of Ilorin, Ilorin

Abstract

The accurate modelling of return unpredictability remains a pivotal challenge in financial econometrics. Traditional models often assume a normal distribution for error terms, which fails to capture the leptokurtic and skewed nature of financial returns. This paper introduces the odd generalized exponential Laplace distribution (OGELAD) as an error distribution tailored for modelling asset return unpredictability. The proposed distribution addresses the limitations of conventional error distributions such as normal (NORM), skew normal (SNORM), normal inverse Gaussian (NIG), and skew generalized error distribution (SGED) in capturing key characteristics of financial returns, such as asymmetry and heavy tails. Using simulated data, the study evaluates the performance of the OGELAD within symmetric and asymmetric volatility models, demonstrating its effectiveness in modelling and forecasting return volatility. Diagnostic tests confirm that all error distributions, including the OGELAD, successfully eliminate ARCH effects from residuals, ensuring robust model performance. Notably, the positive and significant asymmetry parameter in the selected model highlights that positive shocks exert a smaller influence on volatility compared to negative shocks of the same magnitude. This finding underscores the relevance of the proposed distribution in capturing leverage effects observed in financial data. The OGELAD distribution consistently outperformed existing distributions in modelling and forecasting volatility, showcasing its potential for broader applications. It can be extended to multivariate settings for portfolio risk management and applied to high-frequency financial data to test its robustness under varying market conditions.