Analysis and application of a nonstationary time series using a time-dependent pattern entropy

在本研究中，我们尝试使用一种新的分析方法，即时间相依模式熵（T-DPE）来量化非平稳时间序列的不稳定性。用一阶矩和二阶矩刻画汇率日数据的统计特性是困难的。因此，除了分析外汇汇率时间序列的长期平均统计特性外，我们还研究了如何表征时间序列的局部不稳定性。我们应用T-DPE分析了外汇汇率，特别是美元对日元汇率的日变化的不稳定性。发现美元兑日元汇率的时间相关模式熵在以下时期较高：日元从强到弱或从弱到强的转折点之前和之后，以及雷曼冲击之后的时期。

In this research, we attempted the quantification of instability of a nonstationary time series using a time-dependent pattern entropy (T -DPE) as a new analytical method. Characterizing the statistical properties of the daily data of the exchange rate by using the first and second moments is difficult. Therefore, in addition to analyzing the long-time average statistical properties of the time series of foreign exchange rates, we investigated how to characterize the local instability of the time series. We applied T -DPE to analyze the instability of daily variations in foreign exchange rates, in particular, the dollar-yen rate. The time-dependent pattern entropy of the dollar-yen rate was found to be high in the following periods: before and after the turning points of the yen from strong to weak or from weak to strong, and the period after the Lehman shock.