We present a method to construct signatures of periodic-like data. Based on topological considerations, our construction encodes information about the order and values of local extrema. Its main strength is robustness to reparametrisation of the observed signal, so that it depends only on the form of the periodic function. The signature converges as the observation contains increasingly many periods. We show that it can be estimated from the observation of a single time series using bootstrap techniques.

翻译：我们提出一种构建周期类数据签名的方法。基于拓扑考量，该构造编码了局部极值的顺序及其取值信息。其主要优势在于对观测信号重参数化具有鲁棒性，因此仅依赖于周期函数的形式。随着观测包含越来越多周期，该签名趋于收敛。我们证明，利用自助法技术可从单一时间序列观测中对其进行估计。