Warning Ahead of Market Crashes: The Application of Topological Data Analysis

Abstract

Traditional dimensionality reduction methods such as principal component analysis (PCA) and multi-dimensional scaling (MDS), will lead to valuable data losses. The topological data analysis (TDA), however, employed in this paper can deal with multi-dimensional data without losses. It emphasizes the strong robustness to the noise disturbance of the data. We discuss the volatility characteristics of daily returns of major stock indexes in the United States in the 2008 global financial crisis and China in the 2008 and 2015 crashes. We choose 50 trading days as the sliding window and then calculate the L1-norm of "persistent landscape" by TDA method to predict the index collapse. We show that before the financial crisis in 2008 and 2015, the L1-norm of the relevant index increases significantly. And the maximum value of L1-norm emerges more than 1 year before the market collapses. This method has an effective early warning indicator for financial crashes.

Keywords: Topological Data Analysis, Financial Crashes, Persistent Homology, Persistent Landscape, Warning Indicator 1. Introduction