emdr: emdr: Empirical mode decomposition based regression

In PierreMasselot/Library--emdr: Tools for EMD-regression

Description

The emdr package provides functions to decompose time series through empirical mode decomposition (EMD) and use the resulting components (called intrinsic mode functions, IMFs) in a regression analysis.

Details

Functions in the package are roughly divided in three sections:

• MEMD decomposition and description of the resulting IMFs;

• preparing MIMFs being used in a regression function to predict a non-decomposed response variables (denoted EMD-R1);

• predicting one variable's IMF from other variables' IMFs (denoted EMD-R2).

MEMD functions

An analysis usually begins with a call to memd to decompose a multivariate time-series into IMFs. This function supports different modifications from the original algorithm, i.e. ensemble EMD and noise-assisted MEMD to address the issue of mode-mixing. The result from memd is an object of class mimf which can then be analyzed by looking at summarized characteristics through a call to summary.mimf or visually using the plot.mimf method. Finally, imf.test performs an IMF significance test and the method plot.imftest shows the result.

EMD-R1

The EMD-R1 design regresses a non-decomposed response against predictors' IMFs. Thus, any regression function can be used to perform EMD-R1. The function pimf prepares a mimf object as a data.frame to be used in a regression function. It includes lagging the IMFs and adding non-IMF covariates. Since several IMFs can be correlated, it is advised to consider the Lasso regression which can be performed by the function glmnet in the package glmnet. Resulting coefficients can then be standardized by the function sensitivity and displayed by the function plot_emdr.

EMD-R2

In the EMD-R2 design, the response variable is also decomposed and each of its IMFs is regressed against predictors' IMFs of similar frequencies. After a call to memd to jointly decompose the response and predictors, the resulting object can be used in the function emdr2. the result is a list of submodels for each IMF. The function extract.emdr2 extracts any element from each submodel with the coef.emdr2 method for coefficients specifically. As for EMD-R1, these coefficients can then be standardized by the function sensitivity and displayed by the function plot_emdr.

References

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.-C., Tung, C.C., Liu, H.H., 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 903-995.

Rehman, N., Mandic, D.P., 2010. Multivariate empirical mode decomposition. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 466, 1291-1302.

Rehman, N.U., Park, C., Huang, N.E., Mandic, D.P., 2013. EMD Via MEMD: Multivariate Noise-Aided Computation of Standard EMD. Advances in Adaptive Data Analysis 05, 1350007.

Masselot, P., Chebana, F., Belanger, D., St-Hilaire, A., Abdous, B., Gosselin, P., Ouarda, T.B.M.J., 2018. EMD-regression for modelling multi-scale relationships, and application to weather-related cardiovascular mortality. Science of The Total Environment 612, 1018-1029.

PierreMasselot/Library--emdr documentation built on June 19, 2021, 8:58 a.m.