Niigata University, Department of Mathematics, Niigata, 950-2181, Japan.
Kyoto University, GSAIS, Kyoto, 606-8502, Japan.
Sci Rep. 2020 May 21;10(1):8420. doi: 10.1038/s41598-020-65002-3.
We analyze monthly time series of 57 US macroeconomic indicators (18 leading, 30 coincidental, and 9 lagging) and 5 other trade/money indexes. Using novel methods, we confirm statistically significant co-movements among these time series and identify noteworthy economic events. The methods we use are Complex Hilbert Principal Component Analysis (CHPCA) and Rotational Random Shuffling (RRS). We obtain significant complex correlations among the US economic indicators with leads/lags. We then use the Hodge decomposition to obtain the hierarchical order of each time series. The Hodge potential allows us to better understand the lead/lag relationships. Using both CHPCA and Hodge decomposition approaches, we obtain a new lead/lag order of the macroeconomic indicators and perform clustering analysis for positively serially correlated positive and negative changes of the analyzed indicators. We identify collective negative co-movements around the Dot.com bubble in 2001 as well as the Global Financial Crisis (GFC) in October 2008. We also identify important events such as the Hurricane Katrina in August 2005 and the Oil Price Crisis in July 2008. Additionally, we demonstrate that some coincidental and lagging indicators actually show leading indicator characteristics. This suggests that there is a room for existing indicators to be improved.
我们分析了 57 项美国宏观经济指标（18 项领先指标、30 项同步指标和 9 项滞后指标）和 5 项其他贸易/货币指数的月度时间序列。我们使用新颖的方法，确认了这些时间序列之间存在显著的共同运动，并确定了一些值得注意的经济事件。我们使用的方法是复杂希尔伯特主成分分析（CHPCA）和旋转随机置换（RRS）。我们发现美国经济指标之间存在显著的复杂相关性，存在领先/滞后关系。然后，我们使用 Hodge 分解来获得每个时间序列的层次顺序。Hodge 势使我们能够更好地理解领先/滞后关系。我们使用 CHPCA 和 Hodge 分解方法，获得了宏观经济指标的新的领先/滞后顺序，并对分析指标的正序列相关的正变化和负变化进行聚类分析。我们发现，2001 年的网络泡沫和 2008 年 10 月的全球金融危机（GFC）期间存在集体负面共同运动。我们还确定了一些重要事件，如 2005 年 8 月的卡特里娜飓风和 2008 年 7 月的石油价格危机。此外，我们还证明，一些同步指标和滞后指标实际上具有领先指标的特征。这表明现有指标还有改进的空间。
