Enriching the VaR framework to EEMD with an application to the European carbon marketArea for review

Unlike common financial markets, the European carbon market is a typically heterogeneous market, characterized by multiple timescales, and affected by extreme events. The traditional value-at-risk (VaR) with single-timescale fails to deal with the multi-timescale characteristics and the effects of extreme events, which can result in the VaR overestimation for carbon market risk. To measure accurately the risk on the European carbon market, we propose an ensemble empirical mode decomposition (EEMD)-based multiscale VaR approach. First, the EEMD algorithm is utilized to decompose the carbon price return into several intrinsic mode functions (IMFs) with different timescales and a residue, which are modelled, respectively, using the ARMA-Generalized Autoregressive Conditional Heteroscedasticity model to obtain their conditional variances at different timescales. Furthermore, the Iterated Cumulative Sums of Squares algorithm is employed to determine the windows of an extreme event, so as to identify the IMFs influenced by an extreme event and conduct an exponentially weighted moving average on their conditional variations. Finally, the VaRs of various IMFs and the residue are estimated to reconstruct the overall VaR, the validity of which is verified later. Then, we illustrate the results by considering several European carbon futures contracts. Compared with the traditional VaR framework with single timescale, the proposed multiscale VaR-EEMD model can effectively reduce the influences of the heterogeneous environments (such as the influences of extreme events) and obtain a more accurate overall risk measure on the European carbon market. By acquiring the distributions of carbon market risks at different timescales, the proposed multiscale VaR-EEMD estimation is capable of understanding the fluctuation characteristics more comprehensively, which can provide new perspectives for exploring the evolution law of the risks on the European carbon market.