Financial market predictability with tensor decomposition and links forecast.

Inspecting financial markets from a complex network perspective means to extract relationships and interdependencies from stock price time series. Correlation networks have been shown to adequately capture such dependence structures between financial assets. Moreover, researchers have observed modifications in the correlation structure between stock prices in the face of a market turbulence. This happens because financial markets experience sudden regime shifts near phase transitions such as a financial crisis. These abrupt and irregular fluctuations from one state to another lead to an increase of the correlation between the units of the system, lowering the distances between the stocks in a correlation network. The aim of this paper is to predict such abrupt changes by inferring the forthcoming dynamic of stock prices through the prediction of future distances between them. By introducing a tensor decomposition technique to empirically extract complex relationships from prices' time series and using them in a portfolio maximization application, this work first illustrates that, near critical transitions, there exit spatial signals such as an increasing spatial correlation. Secondly using this information in a portfolio optimization context it shows the ability of the methodology in forecasting future stock prices through these spatial signals. The results demonstrate that an optimization approach aiming at minimizing the interconnectedness risk of a portfolio by maximizing the signals produced by tensor decomposition induces investment plans superior to simpler strategies. Trivially speaking portfolios made up of strongly connected assets are more vulnerable to shock events than portfolios of low interconnected assets since heavily connected assets, being close to a transition point, carry a significant amount of interconnectedness risk, i.e. tail events propagate more quickly to these assets.