Granger causality for state-space models
Granger causality for state-space models
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DOI：
10.1103/physreve.91.040101
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发表时间：
2015-04-23
影响因子：
2.4
通讯作者：
Seth, Anil K.
中科院分区：
文献类型：
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作者：
Barnett, Lionel;Seth, Anil K.
格兰杰因果关系长期以来一直是推断各种复杂物理系统随机变量之间因果相互作用的重要方法。然而，人们已经认识到，数据中的移动平均 (MA) 成分对格兰杰因果分析（通常通过自回归 (AR) 建模进行）存在严重干扰。我们通过证明可以根据状态空间（SS）模型的参数简单有效地计算格兰杰因果关系来解决这个问题。由于 SS 模型相当于自回归移动平均模型，因此以这种方式估计的格兰杰因果关系不会因 MA 分量的存在而降低。当数据经过过滤、下采样、用噪声观察或者是高维过程的子过程时，这一点尤其重要，因为所有这些操作（在气候科学、计量经济学和神经科学等不同的应用领域中很常见）都会引发 MA 组件。我们展示了如何通过求解离散代数 Riccati 方程直接从 SS 模型参数计算时域和频域中的条件和无条件格兰杰因果关系。数值模拟表明，由此得出的 Granger 因果关系估计量比 AR 估计量具有更大的统计功效和更小的偏差。我们还讨论了 SS 方法如何促进当前 AR 方法中线性、平稳性和同方差性假设的放松，从而为格兰杰因果分析开辟了潜在的重要新研究领域。
Granger causality has long been a prominent method for inferring causal interactions between stochastic variables for a broad range of complex physical systems. However, it has been recognized that a moving average (MA) component in the data presents a serious confound to Granger causal analysis, as routinely performed via autoregressive (AR) modeling. We solve this problem by demonstrating that Granger causality may be calculated simply and efficiently from the parameters of a state-space (SS) model. Since SS models are equivalent to autoregressive moving average models, Granger causality estimated in this fashion is not degraded by the presence of a MA component. This is of particular significance when the data has been filtered, downsampled, observed with noise, or is a subprocess of a higher dimensional process, since all of these operations-commonplace in application domains as diverse as climate science, econometrics, and the neurosciences-induce a MA component. We show how Granger causality, conditional and unconditional, in both time and frequency domains, may be calculated directly from SS model parameters via solution of a discrete algebraic Riccati equation. Numerical simulations demonstrate that Granger causality estimators thus derived have greater statistical power and smaller bias than AR estimators. We also discuss how the SS approach facilitates relaxation of the assumptions of linearity, stationarity, and homoscedasticity underlying current AR methods, thus opening up potentially significant new areas of research in Granger causal analysis.