Testing for Non-Linear Structures in Artificial and Real-World Financial Data with Recurrence Quantification Analysis

Abstract

Early applications of empirical methods from chaos theory suggested the existence of low dimensional chaotic motion in empirical financial data. However, such results were questioned, and it is then believed that the search for low dimensional chaos in financial data was not successful. On the other hand, at the same time that the hypotheses that raw returns are independent and identically distributed (IID) is often rejected, they indeed present a quite small degree of autocorrelation. These facts suggest that prices in financial markets do not behave completely at random, although their hidden structures seem more complex than those observed in low dimensional chaotic systems. Previous work tested for non-linearity or the presence of low dimensional chaos in artificial financial data generated from the Lux-Marchesi model by means of the BDS and Kaplan tests. Addressing the same model, researchers extended those results by applying Hinich’s bi-spectral and White’s tests and introducing the application of Recurrence Quantification Analysis (RQA) on artificial financial data based on Recurrence Rate, Determinism, Entropy, and Maximal Diagonal Length. Contributing to this research, the present paper has two main goals: (i) to contrast previous findings with an RQA application on data generated by a more evolved of microscopic model of financial markets – the Structural Stochastic Volatility (SSV ) model; and (ii) to extend the RQA investigation above with additional recurrence measures (namely, Divergence, Laminarity, and Maximal Vertical Length) being applied to distinct real-world financial data. The objective is to assess if RQA results could help to distinguish between artificial and real-world data, even if linearity is rejected in both cases. It is shown evidence, in agreement previous findings, to support the rejection of linearity or low dimensional chaotic motion in an artificial financial time series generated from the SSV microscopic model. In addition, it is also shown that that RQA measures can help to discriminate artificial from real-world financial data, at least when specific RQA measures are considered.