Topology Data Analysis Using Mean Persistence Landscapes in Financial Crashes ()
ABSTRACT
Topological
features in high dimensional time series are used to characterize changes in
stock market dynamics over time. We explored the daily log returns of four
major US stock market indices and 10 ETF sectors between January 2010-June 2020. Topological data analysis and
persistence homology were used on two sequences of point cloud data sets the
stock indices and the ETF sectors,
respectively. Using these sequences, the daily log returns, persistence diagrams,
persistence landscapes, and mean landscapes were used to quantify topological
patterns in the multidimensional time series. For example, norms of the
persistence landscapes were generated to detect critical transitions in the
daily log returns. To measure statistical significance, we implemented three
permutation tests with a significance level α = 0.05 to determine if
topological features change within a particular time frame by comparing sliding
windows in the sequence of point cloud data sets. We found that between July 1,
2019 and July 1, 2020, there is evidence of changing structure in the US stock
market. Critical transitions are identified by the statistical properties of
the norms of the persistence landscape between contiguous daily sliding windows
of the stock indices and ETF sector
series.
Share and Cite:
Aguilar, A. and Ensor, K. (2020) Topology Data Analysis Using Mean Persistence Landscapes in Financial Crashes.
Journal of Mathematical Finance,
10, 648-678. doi:
10.4236/jmf.2020.104038.
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