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Topological Data Analysis (TDA) is the collection of mathematical tools thatcapture the structure of shapes in data. Despite computational topology andcomputational geometry, the utilization of TDA in time series and signalprocessing is relatively new. In some recent contributions, TDA has beenutilized as an alternative to the conventional signal processing methods.Specifically, TDA is been considered to deal with noisy signals and timeseries. In these applications, TDA is used to find the shapes in data as themain properties, while the other properties are assumed much less informative.In this paper, we will review recent developments and contributions wheretopological data analysis especially persistent homology has been applied totime series analysis, dynamical systems and signal processing. We will coverproblem statements such as stability determination, risk analysis, systemsbehaviour, and predicting critical transitions in financial markets.

A Short Survey of Topological Data Analysis in Time Series and Systems Analysis