Topological Data Analysis and Applications to Financial Time Series

Specialeforsvar: Jakob Johann Kress

Titel: Topological Data Analysis and Applications to Financial Time Series

Abstract: Data analysis has become ubiquitous in today’s society. In recent years, topological data analysis (TDA) emerged as a new technique using algebraic topology to compute certain invariants of datasets. In this thesis, we give a full account of TDA by
describing the whole spectrum from theory to practice with the latter focusing on time series coming from the financial markets.
We start by introducing the TDA pipeline, which assigns a so-called persistence diagram to a given dataset. We do that by first looking at the underlying mathematical theory and then by analyzing how this pipeline is implemented in computer programs. Thereafter, we proceed to applications by summarizing two papers that both testify meaningfulness of TDA for predictions in the financial markets. Finally, we investigate the intraday trading potential by applying a TDA-based portfolio optimization technique to minute-granular data.

Vejleder: Sergey Avvakumov
Censor:    Iver Mølgaard Ottosen, DTU