Introducinglocalgauss, anRPackage for Estimating and Visualizing Local Gaussian Correlation

Abstract

Quantifying non-linear dependence structures between two random variables is a challenging task. There exist several bona-fide dependence measures able to capture the strength of the non-linear association, but they typically give little information about how the variables are associated. This problem has been recognized by several authors and has given rise to the concept of local measures of dependence. A local measure of dependence is able to capture the "local" dependence structure in a particular region. The idea is that the global dependence structure is better described by a portfolio of local measures of dependence computed in different regions than a one-number measure of dependence. This paper introduces the R package localgauss which estimates and visualizes a measure of local dependence called local Gaussian correlation. The package provides a function for estimation, a function for local independence testing and corresponding functions for visualization purposes, which are all demonstrated with examples.

Oil and stock markets before and after financial crises: A local Gaussian correlation approach

“…An introduction to the R package “localgauss ” for estimation and visualization of local dependence is available in Berentsen, Kleppe, and Tjøstheim ().…”

“…More details concerning the local Gaussian theory can be found in andTjøstheim and Hufthammer (2013).11 An introduction to the R package "localgauss" for estimation and visualization of local dependence is available inBerentsen, Kleppe, and Tjøstheim (2014). BAMPINAS AND PANAGIOTIDIS | 1183…”

Local Gaussian Autocorrelation and Tests for Serial Independence

“…Since, from Section 5, we indicated that the best power is the one after standardization and normalization of the data set, we decided to study these examples after that transformation. To each data set, we apply the function localgauss.indtest() of the R‐package localgauss to obtain the graphics of Figures (for more details, see Berentsen et al , ). To perform the test, we use the test functional .…”

“…In Figures b and b, the point x is magenta if the local correlation ρ n ( x ) is significantly positive, cyan if ρ n ( x ) is significantly negative and white when the null hypothesis is not rejected (see Berentsen et al , , for more details).…”

“…The basic theory for this local construction is given in Tjøstheim and Hufthammer ), including local likelihood estimation depending on a bandwidth parameter b (see , discussion of uniqueness and asymptotic distribution. There are many potential applications, some of which are described in Berentsen et al (), Berentsen and Tjøstheim (), Støve et al () and Støve and Tjøstheim (), and there is a software R‐package for computing ρ ( x ) described in Berentsen et al (). In particular, in Berentsen and Tjøstheim (), the local Gaussian correlation is used to test dependence in the case of pairs of i.i.d.…”