Spurious correlations are common in time-series analysis because simple, low-complexity patterns can produce high Pearson correlations even between unrelated series. We argue that Kolmogorov complexity, interpreted as resistance to compression, provides a principled safeguard against such false positives. Using effective Hausdorff dimension, we show that the probability of accidental correlation between two independent series decays exponentially with their complexity, while noise can inflate observed complexity and must therefore be accounted for in practice. We illustrate these ideas with coupled logistic maps and multivariate fractional Brownian motion (mfBm), where the Hurst parameter \(H\) controls both complexity and Hausdorff dimension \((\dim_H = 2 - H)\). Both models show that false positives are much more common among low-complexity series than among high-complexity ones. We introduce the joint complexity indicator \[ J_{\rm LZ} = \sqrt{\widetilde{C}_{\rm LZ}(x)\widetilde{C}_{\rm LZ}(y)}, \] which captures joint high complexity rather than simple similarity between individual complexities. Its threshold can be calibrated from the mfBm false-positive curve. In logistic maps, \(J_{\rm LZ}\) also anticipates the collapse of individual complexity just before synchronization. We recommend establishing stationarity first, then reporting \(J_{\rm LZ}\) alongside \(ρ\), and treating high correlation among low-complexity series with skepticism.

翻译：时间序列分析中虚假相关十分常见，因为即便是无关序列之间，简单低复杂度的模式也可能产生高皮尔逊相关性。我们认为，柯尔莫哥洛夫复杂度（解释为抗压缩性）为防范这类假阳性提供了理论依据。利用有效豪斯多夫维数，我们证明两个独立序列间偶然相关的概率随其复杂度呈指数衰减，而噪声会人为提升观测复杂度，因此实际应用中必须予以考虑。我们通过耦合逻辑映射与多元分数布朗运动（mfBm）阐释这些概念——其中赫斯特参数\(H\)同时控制复杂度与豪斯多夫维数\((\dim_H = 2 - H)\)。两种模型均表明：相较于高复杂度序列，低复杂度序列的假阳性现象更为普遍。我们提出联合复杂度指标\[ J_{\rm LZ} = \sqrt{\widetilde{C}_{\rm LZ}(x)\widetilde{C}_{\rm LZ}(y)} \]，该指标捕捉的是联合高复杂度而非个体复杂度间的简单相似性。其阈值可通过mfBm假阳性曲线进行校准。在逻辑映射中，\(J_{\rm LZ}\)还能在同步发生前预判个体复杂度的坍缩。我们建议：首先验证序列平稳性，然后同时报告\(J_{\rm LZ}\)与\(ρ\)，并对低复杂度序列间的高相关性持审慎态度。