estim_WLMC {VisualDom}

Estimates the wavelet local multiple correlation

Description

The estim_WLMC function estimates the wavelet local multiple correlation (WLMC) for a set of multivariate time series. The function is based mainly on the work of Fernández-Macho (2018) and to lesser extent in the work of Polanco-Martínez et al. (2020).

Usage

estim_WLMC(inputdata, wf="la8", J, window, M, Ymaxr=NULL)

Arguments

inputdata

A matrix of N columns by P rows: the first column is time (regular/evenly spaced) and the other columns are the variables under study.

wf

Name of the wavelet filter used in the wavelet transform (MODWT) decomposition. There are several wavelet filters to be used, but we use by default the Daubechies orthonormal compactly supported wavelet of length L=8, that is, “la8”.

J

The maximum level of the MODWT decomposition. It is recommended to use log2(N) - 3, where N is the number of rows or elements of inputdata (Fernández-Macho 2018, Polanco-Martínez et al. 2020).

window

Weight or window function, by the default is the Gaussian window (gaussian) but other five window functions can be used, e.g., uniform, Bartlett's triangular, Cleveland's tricube, Wendland's truncated power or Epanechnikov's parabolic. Please look at the function wave.local.multiple.correlation from the R package wavemulcor (Fernandez-Macho 2018).

M

The length of the weight/window function, it is recommended to use N/8, where N is the number of rows or columns (Fernández-Macho 2018, Polanco-Martínez et al. 2020).

Ymaxr

This parameter is used to indicate which variable will be used to maximize the multiple correlation for each wavelet scale, by default is 'NULL', that is, we do not define a priori an specific variable but instead let the WLMC select one (Fernández-Macho 2018, Polanco-Martínez et al. 2020).

Details

The estim_WLMC function estimates the WLMC for multivariate time series including the correlation coefficients and their statistical significance. The estim_WLMC function uses the function wave.local.multiple.correlation (package:wavemulcor) to estimate the wavelet local multiple correlation, and the functions modwt and brick.wall (package:waveslim) to carry out the wavelet decomposition of the time series under study.

Value

Outputs: A list named LISTvals that contains four elements: CORCOEF that contains the correlation coefficients, CIlo and CIup are the lower and upper confidence intervals (CI), and YmaxR contains the indices (numbers from 1 to the number of columns or variables) of the corresponding variables whose correlation is calculated against a linear combination of the rest.

Author(s)

Josué M. Polanco-Martínez (a.k.a. jomopo).
Excellence Unit GECOS, IME, Universidad de Salamanca, Salamanca, SPAIN.
BC3 - Basque Centre for Climate Change, Leioa, SPAIN.
Web1: https://scholar.google.es/citations?user=8djLIhcAAAAJ&hl=en.
Web2: https://www.researchgate.net/profile/Josue-Polanco-Martinez.
Email: [e-mail]
Acknowledgement:
We acknowledge to the Excellence Unit GECOS (reference number CLU-2019-03), Universidad de Salamanca for its funding support.

References

Fernández-Macho, J. (2018). Time-localized wavelet multiple regression and correlation. Physica A: Statistical Mechanics and its Applications, 492, 1226-1238. <URL: doi: 10.1016/j.physa.2017.11.050>.

Polanco-Martínez, J. M., Fernández-Macho, J., & Medina-Elizalde, M. (2020). Dynamic wavelet correlation analysis for multivariate climate time series. Scientific Reports, 10(1), 1-11. <URL: doi: 10.1038/s41598-020-77767-8>.

Whitcher, B., Guttorp, P., & Percival, D. B. (2000). Wavelet analysis of covariance with application to atmospheric time series. Journal of Geophysical Research: Atmospheres, 105(D11), 14941-14962. <URL: doi: 10.1029/2000JD900110>.

Examples

# We reproduce Figure 3 left presented in Polanco-Martínez et al. (2020). 
inputdata  <- rdata_climate
N          <- nrow(inputdata)
wf         <- "la8"               
window     <- "gaussian"          
J          <- 7 
M          <- 168 

output_WLMC <- estim_WLMC(inputdata, wf=wf, J=J, window=window, M=M, Ymaxr=NULL)