Clustering and classification of time series using topological data analysis with applications to finance

Abstract

In this paper, we propose new methods for time series classification and clustering. These methods are based on techniques of Topological Data Analysis (TDA) such as persistent homology and time delay embedding for analysing time-series data. We present a new clustering method SOM-TDA and a new classification method RF-TDA based on TDA. Using SOM-TDA we examine the topological similarities and dissimilarities of some well-known time-series models used in finance. We also use the RF-TDA to examine if the topological features can be used to distinguish between time series models using simulated data. The performance of RF-TDA on the classification task is compared against three other classification methods. We also consider an application of RF-TDA to financial time series classification using real-life price data of stocks belonging to different sectors. RF-TDA is seen to perform quite well in the two experiments based on real-life stock-price data. This implies that the topological features of the time series of stock prices in the different sectors are not identical and have distinctive features that can be discerned through the use of TDA. We also briefly consider multi-class classification using RF-TDA.