Deep Temporal Learning for Carbon Allowance Price Forecasting Toward Carbon Financial Derivatives Pricing: A Multiscale Decomposition and Optimization Framework

Carbon allowance-price forecasting is a multiscale sequence-regression problem: persistent price-level movements coexist with short-term disturbances and associations with observable financial, energy, and environmental indicators. This study evaluates a CEEMDAN–LSTM pipeline in which sample entropy reduces nine intrinsic mode functions (IMFs) to five additive component targets, partial autocorrelation selects component-specific histories, and Spearman coefficients screen CSI 300, the CZCE thermal coal index, and Wuhan AQI as candidate covariates. The component predictors use a common LSTM transition structure with different input configurations. A Harris hawks optimizer incorporating Tent-map exploration and crossover–greedy updates (CRTHHO) searches for the hidden-neuron count and learning rate. On the reported Hubei carbon-market sample of 2009 aligned observations, the updated final-model comparison records MAE = 0.49394, RMSE = 0.88785, and MAPE = 0.01194, versus 0.73014, 1.13677, and 0.01988 for the untuned configuration. These correspond to observed relative error reductions of 32.35%, 21.90%, and 39.94%. The study characterizes the interface between multiscale inputs and recurrent prediction rather than proposing new CEEMDAN or LSTM theory. Results are conditional on the documented evaluation procedure; the available record does not establish complete isolation of test data during every preprocessing and tuning stage. The forecasts concern allowance prices and do not constitute a direct valuation of carbon derivatives.