超前-滞后横截面结构和相关-滞后相关状态转移的检测：应用于通货膨胀和经济增长率的波动
Lead-lag cross-sectional structure and detection of correlated-anticorrelated regime shifts: Application to the volatilities of inflation and economic growth rates
摘要：
我们最近引入了“热最佳路径”（TOP）方法来研究两个时间序列之间的实时超前-滞后结构。TOP方法包括搜索距离矩阵的鲁棒噪声平均最优路径，沿着该路径两个时间序列具有最大的相似性。在这里，我们通过引入一个更一般的距离定义来推广TOP方法，该距离定义考虑了正负相关性之间可能的状态变化。跟踪相关性符号的可能变化的这种概括能够识别从一种约定（或共识）到另一种约定的可能转变。对合成时间序列的数值模拟验证了新的TOP方法，即使在存在大量噪声的情况下，也能达到预期的效果。然后，我们应用它来研究美国通货膨胀率和经济增长率的历史波动之间的依赖结构的惯例的变化。几项措施表明，新的TOP方法显着优于标准的互相关方法。
英文摘要：
We have recently introduced the ``thermal optimal path'' (TOP) method to investigate the real-time lead-lag structure between two time series. The TOP method consists in searching for a robust noise-averaged optimal path of the distance matrix along which the two time series have the greatest similarity. Here, we generalize the TOP method by introducing a more general definition of distance which takes into account possible regime shifts between positive and negative correlations. This generalization to track possible changes of correlation signs is able to identify possible transitions from one convention (or consensus) to another. Numerical simulations on synthetic time series verify that the new TOP method performs as expected even in the presence of substantial noise. We then apply it to investigate changes of convention in the dependence structure between the historical volatilities of the USA inflation rate and economic growth rate. Several measures show that the new TOP method significantly outperforms standard cross-correlation methods.
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