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Register a new userDetecting climate teleconnections with Granger causality
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Filipi Nascimento Silva
Publication date
2020
fields
Physics
and research's language is
English
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Climate system teleconnections, which are far-away climate responses to perturbations or oscillations, are difficult to quantify, yet understanding them is crucial for improving climate predictability. Here we leverage Granger causality in a novel method of identifying teleconnections. Because Granger causality is explicitly defined as a statistical test between two time series, our method allows for immediate interpretation of causal relationships between any two fields and provides an estimate of the timescale of the teleconnection response. We demonstrate the power of this new method by recovering known seasonal precipitation responses to the sea surface temperature pattern associated with the El Ni~{n}o Southern Oscillation, with accuracy comparable to previously used correlation-based methods. By adjusting the maximum lag window, Granger causality can evaluate the strength of the teleconnection (the seasonal precipitation response) on different timescales; the lagged correlation method does not show ability to differentiate signals at different lags. We also identify candidates for previously unexplored teleconnection responses, highlighting the improved sensitivity of this method over previously used ones.
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In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well-established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer across multiple time scales. We show that the multiscale processing of a vector autoregressive (AR) process introduces a moving average (MA) component, and describe how to represent the resulting ARMA process using state space (SS) models and to combine the SS model parameters for computing exact GC values at arbitrarily large time scales. We exploit the theoretical formulation to identify peculiar features of multiscale GC in basic AR processes, and demonstrate with numerical simulations the much larger estimation accuracy of the SS approach compared with pure AR modeling of filtered and downsampled data. The improved computational reliability is exploited to disclose meaningful multiscale patterns of information transfer between global temperature and carbon dioxide concentration time series, both in paleoclimate and in recent years.
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the local Granger causality, i.e. the profile of the information transfer at each discrete time point in Gaussian processes; in this frame Granger causality is the average of its local version. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear complex systems studied in the Gaussian approximation.
A high degree of consensus exists in the climate sciences over the role that human interference with the atmosphere is playing in changing the climate. Following the Paris Agreement, a similar consensus exists in the policy community over the urgency of policy solutions to the climate problem. The context for climate policy is thus moving from agenda setting, which has now been mostly established, to impact assessment, in which we identify policy pathways to implement the Paris Agreement. Most integrated assessment models currently used to address the economic and technical feasibility of avoiding climate change are based on engineering perspectives with a normative systems optimisation philosophy, suitable for agenda setting, but unsuitable to assess the socio-economic impacts of a realistic baskets of climate policies. Here, we introduce a fully descriptive, simulation-based integrated assessment model designed specifically to assess policies, formed by the combination of (1) a highly disaggregated macro-econometric simulation of the global economy based on time series regressions (E3ME), (2) a family of bottom-up evolutionary simulations of technology diffusion based on cross-sectional discrete choice models (FTT), and (3) a carbon cycle and atmosphere circulation model of intermediate complexity (GENIE-1). We use this combined model to create a detailed global and sectoral policy map and scenario that sets the economy on a pathway that achieves the goals of the Paris Agreement with >66% probability of not exceeding 2$^circ$C of global warming. We propose a blueprint for a new role for integrated assessment models in this upcoming policy assessment context.
An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, conditions are then derived under which Granger causality between them can be reliably inferred from the second order moments of the quantized processes. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform, uniform or high resolution quantizers. This approach does not require the statistics of the underlying Gaussian signals to be estimated, or a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.
Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate locally stationary processes. Our proposed local Granger causality approach captures time-evolving causality relationships in nonstationary processes. The proposed local Granger causality is well represented in the frequency domain and estimated based on the parametric time-varying spectral density matrix using the local Whittle likelihood. Under regularity conditions, we demonstrate that the estimators converge to multivariate normal in distribution. Additionally, the test statistic for the local Granger causality is shown to be asymptotically distributed as a quadratic form of a multivariate normal distribution. The finite sample performance is confirmed with several simulation studies for multivariate time-varying autoregressive models. For practical demonstration, the proposed local Granger causality method uncovered new functional connectivity relationships between channels in brain signals. Moreover, the method was able to identify structural changes in financial data.
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