Wavelet decomposition for time series: Determining input model by using mRMR criterion

Abstract

Determining the level of decomposition and coefficients used as input in the wavelet modeling for time series has become an interesting problem in recent years. In this paper, the detail and scaling coefficients that would be candidates of input determined based on the value of Mutual Information. Coefficients generated through decomposition with Maximal Overlap Discrete Wavelet Transform (MODWT) were sorted by Minimal Redundancy Maximal Relevance (mRMR) criteria, then they were performed using an input modeling that had the largest value of Mutual Information in order to obtain the predicted value and the residual of the initial (unrestricted) model. Input was then added one based on the ranking of mRMR. If additional input no longer produced a significant decrease of the residual, then process was stopped and the optimal model was obtained. This technique proposed was applied in both generated random and financial time series data.