Modelling volatility and return based on a two-stage Log-BiACARR framework and intraday information: Evidence from Guangdong and Hubei carbon emissions trading markets
Author Identifier (ORCID)
David Allen: https://orcid.org/0000-0001-7782-0865
Abstract
This paper proposes a novel two-stage framework to analyse volatility dynamics and return heteroskedasticity in the Guangdong and Hubei carbon emissions trading markets. In the first stage, volatilities are computed using the Roger-Satchell (RS) estimator, which efficiently captures intraday price variability. These RS volatilities are then modelled using the logarithmic asymmetric bilinear conditional autoregressive range (Log-BiACARR) model. This model integrates bilinear and asymmetric components while ensuring the positivity of volatilities, allowing for the modelling of nonlinear persistence and volatility dynamics. In the second stage, a two-stage Log-BiACARR-return model is developed by incorporating autoregressive returns and a fitted RS volatility term, while all fitted RS volatilities obtained from the first-stage Log-BiACARR model are jointly employed to capture return heteroskedasticity. Building on this framework, the models enable precise estimation of volatility-at-risk (VoaR) and value-at-risk (VaR). Empirical analyses for both markets demonstrate strong in-sample and out-of-sample performance. The results highlight the importance of the bilinear component and confirm the existence of a return-volatility feedback mechanism. Moreover, the two-stage model employs a skewed generalised error distribution in modelling heavy-tailed, leptokurtic, and asymmetric returns, effectively capturing the heteroskedasticity of returns. VoaR and VaR values are tested using the Kupiec test, underscoring the applicability of the proposed framework. Our results offer a new basis for evaluating carbon trading prices and their volatilities, providing valuable insights for market participants, encouraging environmentally responsible behaviour, and contributing to a more sustainable transition within the framework of climate policy.
Keywords
Asymmetric range-based model, Carbon emissions trading, Prices, Roger-Satchell estimator, Two-stage model, Volatility
Document Type
Journal Article
Date of Publication
1-1-2026
Volume
681
Publication Title
Physica A: Statistical Mechanics and its Applications
Publisher
Elsevier
School
School of Business and Law
Funding Information
Ministry of Higher Education, Malaysia (FP067\u20132023)
Copyright
subscription content
Comments
He, J., Ng, K., Peiris, S., & Allen, D. (2025). Modelling volatility and return based on a two-stage Log-BiACARR framework and intraday information: Evidence from Guangdong and Hubei carbon emissions trading markets. Physica A: Statistical Mechanics and its Applications, 681, 131097. https://doi.org/10.1016/j.physa.2025.131097