Granger causality in the frequency domain: derivation and applications

Abstract

autores contribuíram igualmente na escrita e elaboração do presente trabalho.Físicas e físicos têm começado a trabalhar em áreas onde é necessária a análise de sinais ruidosos. Nessas áreas, tais como a Economia, a Neurociência e a Física, a noção de causalidade deve ser interpretada como uma medida estatística. Introduzimos ao leitor leigo a causalidade de Granger entre duas séries temporais e ilustramos como calculá-la: um sinal X "Granger-causa" Y se a observação do passado de X aumenta a previsibilidade do futuro de Y em comparação com o que é possível prever apenas pela observação do passado de Y . Em outras palavras, para haver causalidade de Granger entre dois sinais basta que a informação do passado de um melhore a previsão do futuro de outro, mesmo na ausência de mecanismos físicos de interação. Apresentamos a derivação da causalidade de Granger nos domínios do tempo e da frequência e damos exemplos numéricos através de um método nãoparamétrico no domínio da frequência. Métodos paramétricos são abordados no Apêndice. Discutimos limitações e aplicações desse método e outras alternativas para medir causalidade. Palavras-chave: Causalidade de Granger, processo autoregressivo, causalidade de Granger condicional, estimação não-paramétrica Physicists are starting to work in areas where noisy signal analysis is required. In these fields, such as Economics, Neuroscience, and Physics, the notion of causality should be interpreted as a statistical measure. We introduce to the lay reader the Granger causality between two time series and illustrate ways of calculating it: a signal X "Granger-causes" a signal Y if the observation of the past of X increases the predictability of the future of Y when compared to the same prediction done with the past of Y alone. In other words, for Granger causality between two quantities it suffices that information extracted from the past of one of them improves the forecast of the future of the other, even in the absence of any physical mechanism of interaction. We present derivations of the Granger causality measure in the time and frequency domains and give numerical examples using a non-parametric estimation method in the frequency domain. Parametric methods are addressed in the Appendix. We discuss the limitations and applications of this method and other alternatives to measure causality.

A Road Behavior Pattern-Detection Model in Querétaro City Streets by the Use of Shape Descriptors

“…Granger causality [49] is a statistical concept of causality based on prediction given two stochastic signals or variables, X t and Y t . In this concept, X t (Granger) causes a variable Y t .…”

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

“…Wilson's method has been used before in connection with other Granger causality descriptions both related (Jachan et al, 2009) and directly unrelated (Dhamala et al, 2008) to PDC/DTF descriptions. It has the advantage that it can be applied to nonparametric spectral estimates, whether they are obtained by periodogram smoothing (Percival and Walden, 1993) or other means like wavelets (Lima et al, 2020).…”

“…The reader may obtain a working Python implementation in (Lima et al, 2020). Here a similar Matlab version was used.…”

Computational study of thalamocortical interactions: simulating oscillatory activity

“…These next sections about Granger Causality are adaptations of the educational article published by me and colleagues (Lima et al, 2020) entitled "Granger causality in the frequency domain: derivation and applications".…”

“…The algorithm and codes used to measure the GC defined above were described in Lima et al (2020) and the code is available at https://github.com/ ViniciusLima94/pyGC.git.…”