Fast and effective pseudo transfer entropy for bivariate data-driven causal inference

Abstract

Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters limit their applicability. Here we propose a computationally efficient measure for causality testing, which we refer to as pseudo transfer entropy (pTE), that we derive from the standard definition of transfer entropy (TE) by using a Gaussian approximation. We demonstrate the power of the pTE measure on simulated and on real-world data. In all cases we find that pTE returns results that are very similar to those returned by Granger causality (GC). Importantly, for short time series, pTE combined with time-shifted (T-S) surrogates for significance testing strongly reduces the computational cost with respect to the widely used iterative amplitude adjusted Fourier transform (IAAFT) surrogate testing. For example, for time series of 100 data points, pTE and T-S reduce the computational time by $$82\%$$ 82 % with respect to GC and IAAFT. We also show that pTE is robust against observational noise. Therefore, we argue that the causal inference approach proposed here will be extremely valuable when causality networks need to be inferred from the analysis of a large number of short time series.

What do large‐scale patterns teach us about extreme precipitation over the Mediterranean at medium‐ and extended‐range forecasts?

“…To further advance this direction, it would be useful to research additional aspects:Are there teleconnections influencing the occurrence of the nine Mediterranean patterns? Such a question can be answered by exploring causal relationships between the patterns and various climatic indices (e.g., Runge et al ., 2019; Di Capua et al ., 2020; Silini and Masoller, 2021) Are there sources of predictability that give higher confidence for the forecasts of the patterns at extended‐range lead times? What would be the benefits of using more localized large‐scale patterns for different subdomains in the Mediterranean, considering, for example, country‐wise analysis? How skilful is indirect EPE forecasting when using other predictors, such as water vapour flux that is highly related to precipitation (Lavers et al ., 2011; Lavers et al ., 2014; Lavers et al ., 2016a; Lavers et al ., 2016b; Lavers et al ., 2017; Lavers et al ., 2018)? Answering such questions can provide guidelines about which predictor is beneficial for different spatiotemporal resolutions, locations, and forecasting horizons, making better use of already available NWP model outputs. This can ultimately support the development of new operational products towards seamless predictions of extreme precipitation that will provide higher confidence to decision‐makers and users in different sectors.…”

“…• Are there teleconnections influencing the occurrence of the nine Mediterranean patterns? Such a question can be answered by exploring causal relationships between the patterns and various climatic indices (e.g., Runge et al, 2019;Di Capua et al, 2020;Silini and Masoller, 2021) • Are there sources of predictability that give higher confidence for the forecasts of the patterns at extended-range lead times?…”

Ecoregion based attribution analysis of the influence of several fire danger indices on the amount of burned area at a global scale by means of pseudo transfer entropy

“…Once the monthly data is computed, an analysis of the causality from fire danger indices to the fire burned area is performed using a recent fast and effective metric called pseudo transfer entropy (pTE) (Silini 2021). Given…”

Assessing causal dependencies in climatic indices

“…Recently, two of us used a measure, referred to as pseudo transfer entropy (pTE) (Silini and Masoller 2021) that is a linear estimator of the TE, as it is the analytical expression of TE for Gaussian processes. Previous works have used the Gaussian TE expression to study, using the wavelet transform, causality across rainfall time scales (Molini et al 2010), and to study, using the Hilbert transform, phase-amplitude coupling in a century long record of data of daily surface air temperature from various European locations (Palus 2014).…”

“…The pTE measure has two parameters that have to be properly selected: the order of the model used to represent the data, and the lag time of information transfer. In Silini and Masoller (2021) the pTE results were validated using model generated data (where the underlying causality was known) and then, it was applied to the analysis of the tele-connection between the Central Pacific and the Indian Ocean, as inferred from the bivariate analysis of the monthly-sampled time series of NINO3.4 and All India Rainfall (AIR) indices. While pTE and GC only detected the dominant causality (NINO3.4 → AIR), TE detected both.…”