Irreversibility of financial time series: A graph-theoretical approach

• We make use of visibility graph analysis to investigate the irreversibility properties of financial time series.
• We find that stock prices are time irreversible, and the amount of irreversibility fluctuates in time.
• We cluster years of high and low irreversibility that match unstable (crisis/bubbles) and stable financial years.
• We also rank companies according to aggregated irreversibility values. This measure is not correlated with financial volatility.
• This measure can be directly applied to non-stationary processes, allowing a link with entropy production.

The relation between time series irreversibility and entropy production has been recently investigated in thermodynamic systems operating away from equilibrium. In this work we explore this concept in the context of financial time series. We make use of visibility algorithms to quantify, in graph-theoretical terms, time irreversibility of 35 financial indices evolving over the period 1998–2012. We show that this metric is complementary to standard measures based on volatility and exploit it to both classify periods of financial stress and to rank companies accordingly. We then validate this approach by finding that a projection in principal components space of financial years, based on time irreversibility features, clusters together periods of financial stress from stable periods. Relations between irreversibility, efficiency and predictability are briefly discussed.