Modelling Regime-Specific Dependence Structure and Investment Risk Implications in Stock Markets using Copula-Switching GARCH-GED Models

Abstract

A well-known traditional GARCH model assumes normal innovations that do not satisfactorily model sudden variations usually caused by economic tremors or disturbances. This has necessitated the need to develop non-linear, distributional and robust models. In this study, a new set of GARCH models with smooth transition non-linearities and novel innovation distributions are developed to improve the modeling and forecasting of stock returns volatilities in the Nigeria /US stock markets’ Daily data on Heating Oil, Crude Oil, and Gasoline regular spot prices (Naira/US per Dollar) from 1985 to 2025 were obtained from the U.S. Energy Information Administration (EIA) website (https://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm).  This study was carried out using copula-based regime switching GARCH Generalized Error distribution (GED) model and a hidden Markov model. The copula switching GARCH (CoS GARCH) framework showed that the spot prices of crude oil, heating oil and gasoline demonstrated distinct patterns of volatility clustering and distributions with heavy and notable interdependence among different regimes. The estimated transition probability matrix indicated that the Markov chain associated with the volatility states displayed significant persistence. The equations for the conditional means indicated that returns were marginally different across the regimes, which aligns with the established observation that energy price returns have small means compared with their variances. The findings of the study therefore established the presence of heavy tails, clustering of volatility, structural changes, and significant interdependence in energy markets.