A novel interpretable model ensemble multivariate fast iterative filtering and temporal fusion transform for carbon price forecasting

Abstract

The accurate forecasts of carbon prices can help policymakers and enterprises further understand the laws of carbon price fluctuations and formulate related policies and investment strategies. Nowadays, many carbon price prediction models have been proposed. However, some models ignore the time–frequency relationship when considering exogenous variables and fail to measure their importance to the forecasting results, leading to unsatisfactory results. Therefore, this study proposes a novel hybrid model for carbon price forecasting on the basis of advanced multidimensional time series decomposition techniques and interpretable multifactor models. In the proposed model, multivariate fast iterative filtering is used to decompose carbon price and its exogenous variable sequence into several intrinsic mode functions, which can overcome the nonlinearity and nonstationarity of carbon prices and obtain their intrinsic characteristics. Meanwhile, temporal fusion transform (TFT) is used to interpret predictions for multivariate time series. TFT is a new attention-based deep learning model combining high-performance multihorizon prediction and interpretability and can adaptively select the optimal features for carbon price prediction. Five carbon markets in Guangdong, Beijing, Shanghai, Hubei, and Shenzhen are selected for experimental studies. Empirical results indicate that the proposed model outperforms the compared benchmark models in all performance metrics. In the interpretable output of TFT, the prediction of the high-frequency part requires the participation of exogenous variables and has a long time dependence; for the middle and low-frequency part, only using the carbon price itself and a short time step can lead to good results. This finding can inform future research on carbon price forecasting and help policymakers.