论文标题
从转移熵的P值的异步时间序列之间的各个时间尺度上铅滞后的统计推断
Statistical inference of lead-lag at various timescales between asynchronous time series from p-values of transfer entropy
论文作者
论文摘要
符号转移熵是一种强大的非参数工具，可检测时间序列之间的铅滞后。由于传递熵分布的封闭表达对于有限大小的样品不知道，因此通常使用引导程序进行统计测试，这些引导程序阻止了长时间序列之间的大铅滞后网络的推断。另一方面，已知两个时间序列之间转移熵的渐近分布。在这项工作中，我们得出了一个时间序列的测试的渐近分布，其转移熵比目标时间序列的另一个转移熵更大。然后，我们通过基准测量小样本限制的两种测试的收敛速度。然后，我们引入转移时间序列之间的转移熵，该熵允许测量信息传输最大和消失的时间范围。我们最终将这些方法应用于数百个股票的逐个价格变化，从而产生了非平凡的统计验证网络。
Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often performed with bootstraps whose slowness prevents the inference of large lead-lag networks between long time series. On the other hand, the asymptotic distribution of Transfer Entropy between two time series is known. In this work, we derive the asymptotic distribution of the test for one time series having a larger Transfer Entropy than another one on a target time series. We then measure the convergence speed of both tests in the small sample size limits via benchmarks. We then introduce Transfer Entropy between time-shifted time series, which allows to measure the timescale at which information transfer is maximal and vanishes. We finally apply these methods to tick-by-tick price changes of several hundreds of stocks, yielding non-trivial statistically validated networks.
