*Tid:* **20 december 2017 kl 15.35-16.10.**
**Seminarierummet F11**, Institutionen för
matematik, KTH, Lindstedtsvägen 22.
*Föredragshållare:*
**
Patrick Truong
**
**Title:**
An exploration of topological properties of high-frequency one-dimensional financial time series data using TDA
**Abstract:**
Topological data analysis has been shown to provide novel insight in many natural sciences. To our knowledge, the area is however relatively unstudied on financial data. This thesis explores the use of topological data analysis on one dimensional financial time series. Takens embedding theorem is used to transform a one dimensional time series to an m-dimensional point cloud, where m is the embedding dimension. The point cloud of the time series represents the states of the dynamical system of the one dimensional time series. To see how the topology of the states differs in different partitions of the time series, sliding window technique is used. The point cloud of the partitions is then reduced to three dimensions by PCA to allow for computationally feasible persistent homology calculation. Synthetic examples are shown to illustrate the process. Lastly, persistence landscapes are used to allow for statistical analysis of the topological features. The topological properties of financial data are compared with quantum noise data to see if the properties differ from noise. Complexity calculations are performed on both datasets to further investigate the differences between high-frequency FX data and noise. The results suggest that high-frequency FX data differs from the quantum noise data and that there might be some property other than mutual information of financial data which topological data analysis uncovers.
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