Topological signatures of periodic-like signals
Copyright policy )Topological signatures of periodic-like signals
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.
- University of Nantes France
- Université de Nantes France
- Département de Mathématiques France
- Laboratoire de Mathématiques Jean Leray France
- Centre Inria de l'Université Paris-Saclay France
Time series, [STAT.ME] Statistics [stat]/Methodology [stat.ME], Dependent data, Topological data analysis, limit theorems, Mathematics - Statistics Theory, Statistics Theory (math.ST), Functional data, Limit theorems, Persistent homology and applications, topological data analysis, persistent homology, 004, MSC, Extreme value theory; extremal stochastic processes, Time series, auto-correlation, regression, etc. in statistics (GARCH), [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Persistent homology, time series, [STAT.ME]Statistics [stat]/Methodology [stat.ME], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], functional data, dependent data
Time series, [STAT.ME] Statistics [stat]/Methodology [stat.ME], Dependent data, Topological data analysis, limit theorems, Mathematics - Statistics Theory, Statistics Theory (math.ST), Functional data, Limit theorems, Persistent homology and applications, topological data analysis, persistent homology, 004, MSC, Extreme value theory; extremal stochastic processes, Time series, auto-correlation, regression, etc. in statistics (GARCH), [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Persistent homology, time series, [STAT.ME]Statistics [stat]/Methodology [stat.ME], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], functional data, dependent data
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