Carbon prices follow a stochastic process of complex time series with nonstationary and nonlinear characteristics, making forecasting \(CO_2\) emission prices an important and difficult task for policymakers and market participants. Existing literature has focused on highly precise point forecasting, but in most cases, it cannot correctly solve the uncertainties associated with carbon price datasets. Because the volatility of the European Union’s Emissions Trading Scheme (EU ETS) has time-series characteristics, as well as long-term memory, volatility aggregation, asymmetry, and nonlinearity, this study proposes an ETS volatility prediction model by combining convolutional neural networks (CNN), and long short-term memory (LSTM) network and generalized autoregressive conditional heteroscedasticity (GARCH) family models. The proposed Convolutional Neural Networks-based methodology assumes sparse and noisy input data. The presented method employs Compressed Sensing methodology, which assumes that noisy time series are incomplete signals that can be reconstructed using CS reconstruction algorithms. Denoised training sets are more relevant in terms of the prediction performance of NN-based forecasting models. The proposed technique is robust, according to empirical results.