Comparison of six methods for the detection of causality in a bivariate time series

Abstract

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Testing for Dynamical Dependence: Application to the Surface Mass Balance Over Antarctica

“…Another methodology is based on the flow of information, derived from the notion of information entropy introduced originally by Shannon (). This approach has been advocated for many years (e.g., Abarbanel et al, ; Bianco‐Martinez & Baptista, ; Deza et al, ; Hlavackova‐Schindler et al, ; Krakovská et al, ; Liang & Kleeman, ; Runge et al, ; Schreiber, ; Vastano & Swinney, ). In this framework, a rigorous formalism for the transfer of information from one set of variables of a dynamical system to another has been recently put forward (Liang & Kleeman, ; ).…”

Inferring causality from highly noisy uni-directionally coupled chaotic oscillators with small frequency mismatch

“…To demonstrate the performance of the method we considered two examples of uni-directionally connected chaotic Rössler systems [12] with small frequency mismatch and having variable coupling strengths. The oscillators were coupled via a one-way driving relationship between variable of the driving system and variable of…”

“…However, the appropriateness of direct application to nonlinear systems depends on the specific problem to be analyzed [4][5][6]. Therefore, new approaches have been proposed, including nonlinear extensions of Granger causality [4], transfer entropy [7], conditional mutual information [8], evolution map approach (EMA) [9,10], convergent cross-mapping (CCM) method [5,11,12], and measures evaluating distances of conditioned neighbours in reconstructed state spaces [13][14][15][16][17], to name a few. A comprehensive review can be found in Focus Issue [18].…”

Transfer entropy computation using the Perron-Frobenius operator

“…O. Rössler proposed his system in 1976 as a simpler version of the Lorenz attractor in order to more easily study its chaotic properties. Here we study a coupled version of both systems also studied in [42,47], generated by the vector fielḋ x1 = −6 (x2 + x3) ,…”

“…The choice of the size of the intervals along each axis is adapted to the size of the attractor and the number of points available. Following [42], if N is the number of points furnishing the (embedded) attractor and d is the embedding dimension, the number of intervals along each axis is taken as N int = min ceil N 1/(d+1) , n max , where ceil(·) denotes the ceiling and n max is taken to be 9 for d = 3 and 4 for d = 6. If {p i } is the set of points furnishing the attractor (it could either be the actual set of points in the embedding or the result of the sampling of the simplices in the triangulation), the size of the intervals along the a-th axis is chosen as follows: Let O a = 1 − 1 10 Nint min {(p i ) a |1 ≤ i ≤ N } and T a = 1 + 1 10 Nint max {(p i ) a |1 ≤ i ≤ N }.…”