Applying Empirical Mode Decomposition and mutual information to separate stochastic and deterministic influences embedded in signals

• New approach to improve time series modeling.
• Decomposition of stochastic and deterministic influences.
• The paper presents a proof of Empirical Mode Decomposition that works as a filter bank.
• Experiments were conducted on synthetic and real-world signals.

Empirical Mode Decomposition (EMD) is a method to decompose signals into Intrinsic Mode Functions (IMFs) to be analyzed in terms of instantaneous frequencies and amplitudes. By comparing the phase spectra of IMFs, we observed that a subset of them contains more stochastic influences while the other is predominantly deterministic. Considering this observation, we claim that IMFs can be combined to form two additive components: one deterministic and another stochastic. Having both components separated, researchers can improve data modeling as well as forecasting. In this context, this paper presents a new approach to separate deterministic from stochastic influences embedded in signals, considering the mutual information contained in phase spectra of consecutive IMFs. As previous step of this study, we also proved that EMD works as a filter bank.