Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode

Abstract

We investigate the emergence of a structure in the correlation matrix of assets' returns as the time-horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. Result crucially depends on whether the data is restricted to the "internal" dynamics of the market, where the "center of mass" motion (the market mode) is removed or not. If the market mode is not removed, we find that the structure emerges, as the time-horizon increases, from splitting a single large cluster. In NYSE we find that when the market mode is removed, the structure of correlation at the daily scale is already well defined at the 5 minutes time-horizon, and this structure accounts for 80 % of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.

Relation between Financial Market Structure and the Real Economy: Comparison between Clustering Methods

“…After estimating the coefficients α i and β i with a linear regression, the residuals c i (t) can be calculated and used to evaluate the new correlation matrix [27]. We denote this matrix, estimated in the time window T k with ρ R (T k ).…”

“…In the non-detrended case, we find that the highest values of Adjusted Rand Index, R For what concerns the detrended case, we notice first of all that the maximum values of R adj increase for all the methods. The natural explanation for this is that the market mode, driving Financial Market Structure and the Real Economy all the stocks regardless of their industrial supersector, hides to some extent the ICB structure [27]. The CL shows now the highest degree of similarity (0.510), followed by the AL (0.48, showing the most remarkable increase with respect to the non-detrended case), the k-medoids (0.467) and DBHT (0.444).…”

Dynamic instability in generic model of multi-assets markets

“…The largest eigenvalue of the correlation matrix, in turn, undergoes a non-trivial dynamics with sharp rises during crashes (Drozdz et al, 2001). Actually the structure (Bonanno et al, 2003) and dynamics (Potters et al, 2005) of financial correlations is much more complex than that captured by a single eigenvalue and postulated by one factor models (see also Onnela et al, 2003;Borghesi et al, 2007). This paper focuses, in particular, on the time dependence of financial correlations.…”

The Japanese Economy in Crises: A Time Series Segmentation Study

“…However, its application in econophysics took off right after Mantegna and coworkers showed that the MST is a robust caricature of the cross correlations matrix (Mantegna, 1999;Bonanno et al, 2000;Miccichè et al, 2003). The MST is now part of the basic tool suite for statistical analysis of financial market data Jung et al, 2006;Brida and Risso, 2007;Borghesi et al, 2007;Brida and Risso, 2008;Eom et al, 2009;Brida and Risso, 2010). In particular, Onnela et al (2003a,b,c), used MSTs extensively to study the dynamics of cross correlations during market crashes, while many others used clustering techniques based on the MST to discover different sectors in a stock market (Onnela et al, 2004;Bonanno et al, 2004;Boginski et al, 2005;Tumminello et al, 2007;Coelho et al, 2007b;Jung et al, 2008).…”