Modelling volatility and return based on a two-stage Log-BiACARR framework and intraday information: Evidence from Guangdong and Hubei carbon emissions trading markets

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.