差异区域平衡法探索时间序列变化的因果关系

针对探索时间序列之间随时间变化的因果关系问题，在每个窗口进行Granger因果检测的滑动时间窗口方法是求解该问题的常用方法，但其性能对窗宽敏感，不合适的窗宽很可能导致低性能。该文提出一种差异区域平衡方法，首先计算当前滑动窗口W内序列的波动程度Sw并作为波动界，计算窗口W的前向相邻区域U内序列的波动程度Su。然后，实施前向探索策略:若Su未超过Sw，则实施不同长度区域的平衡检测方案，即对窗口W、对窗口W与U的合并区域、对窗口W与后向相邻区域V的合并区域这3种不同长度的差异区域，分别进行时间序列之间因果关系的检测；若Su超过Sw，则实施上述平衡检测方案时，其中区域U和V的长度取相同值。最后，将窗口W的多次检测结果进行综合后输出。新方法将不同长度区域的结果进行综合，能够降低方法的性能对窗宽的敏感性，保障最终结果的准确性和稳定性。在1个模拟数据集和4个真实数据集上的实验结果显示，该文方法能有效地揭示出时间序列之间随时间变化的因果关系，在正确率高且性能稳定的综合性能上优于对比方法。

Different-region Balance Method for Exploring Varying Causal Relations Between Time Series

For discovering time-varying causal relations between time series, a common method is the sliding-window method with Granger causal tests on every window. However, the method performance is sensitive to window sizes, and an unsuitable size probably leads to poor performance. The different-region balance method is proposed. The variation degree of time series in current sliding window W (called variation bound Sw) is first computed, and the degree Su in front neighbor region U of W is computed. Then a forward exploring strategy is adopted: when Su≤Sw, a different-length-region balance test measure is carried out, i.e., causal-relation tests respectively in window W, combined region W and U, and combined window W and back neighbor region V of W; when Su>Sw, it uses the above-mentioned measure where region V has the same length as region U; Finally, in each region, all the test results are synthesized to give a final result. The new method combines the results from different-length regions to reduce its sensitivity to window sizes, and guarantees the accuracy and stability of final results. The experiments on one simulated data set and four real data sets show that, the new method can discover time-varying causal relations between time series effectively, and outperforms the compared methods on the balance performance of high accuracy and stability.