14 research outputs found
Community detection for correlation matrices
A challenging problem in the study of complex systems is that of resolving,
without prior information, the emergent, mesoscopic organization determined by
groups of units whose dynamical activity is more strongly correlated internally
than with the rest of the system. The existing techniques to filter
correlations are not explicitly oriented towards identifying such modules and
can suffer from an unavoidable information loss. A promising alternative is
that of employing community detection techniques developed in network theory.
Unfortunately, this approach has focused predominantly on replacing network
data with correlation matrices, a procedure that tends to be intrinsically
biased due to its inconsistency with the null hypotheses underlying the
existing algorithms. Here we introduce, via a consistent redefinition of null
models based on random matrix theory, the appropriate correlation-based
counterparts of the most popular community detection techniques. Our methods
can filter out both unit-specific noise and system-wide dependencies, and the
resulting communities are internally correlated and mutually anti-correlated.
We also implement multiresolution and multifrequency approaches revealing
hierarchically nested sub-communities with `hard' cores and `soft' peripheries.
We apply our techniques to several financial time series and identify
mesoscopic groups of stocks which are irreducible to a standard, sectorial
taxonomy, detect `soft stocks' that alternate between communities, and discuss
implications for portfolio optimization and risk management.Comment: Final version, accepted for publication on PR
Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations
The mesoscopic organization of complex systems, from financial markets to the
brain, is an intermediate between the microscopic dynamics of individual units
(stocks or neurons, in the mentioned cases), and the macroscopic dynamics of
the system as a whole. The organization is determined by "communities" of units
whose dynamics, represented by time series of activity, is more strongly
correlated internally than with the rest of the system. Recent studies have
shown that the binary projections of various financial and neural time series
exhibit nontrivial dynamical features that resemble those of the original data.
This implies that a significant piece of information is encoded into the binary
projection (i.e. the sign) of such increments. Here, we explore whether the
binary signatures of multiple time series can replicate the same complex
community organization of the financial market, as the original weighted time
series. We adopt a method that has been specifically designed to detect
communities from cross-correlation matrices of time series data. Our analysis
shows that the simpler binary representation leads to a community structure
that is almost identical with that obtained using the full weighted
representation. These results confirm that binary projections of financial time
series contain significant structural information.Comment: 15 pages, 7 figure
Wealth management in Singapore
<p>Each community is labelled with the number of stocks, and the pie chart represents the relative composition of each community based on the industry sectors of the constituent stocks (color legend in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133679#pone.0133679.t001" target="_blank">Table 1</a>). The inter-community link weights are negative, indicating that the communities are all residually anti-correlated.</p
Monitoring the Morphology of M87* in 2009–2017 with the Event Horizon Telescope
The Event Horizon Telescope (EHT) has recently delivered the first resolved images of M87*, the supermassive black hole in the center of the M87 galaxy. These images were produced using 230 GHz observations performed in 2017 April. Additional observations are required to investigate the persistence of the primary image feature—a ring with azimuthal brightness asymmetry—and to quantify the image variability on event horizon scales. To address this need, we analyze M87* data collected with prototype EHT arrays in 2009, 2011, 2012, and 2013. While these observations do not contain enough information to produce images, they are sufficient to constrain simple geometric models. We develop a modeling approach based on the framework utilized for the 2017 EHT data analysis and validate our procedures using synthetic data. Applying the same approach to the observational data sets, we find the M87* morphology in 2009–2017 to be consistent with a persistent asymmetric ring of ~40 μas diameter. The position angle of the peak intensity varies in time. In particular, we find a significant difference between the position angle measured in 2013 and 2017. These variations are in broad agreement with predictions of a subset of general relativistic magnetohydrodynamic simulations. We show that quantifying the variability across multiple observational epochs has the potential to constrain the physical properties of the source, such as the accretion state or the black hole spin
Communities of the Nikkei 225 (daily closing prices from 2001 to 2011) generated using the modified Louvain algorithm [7].
<p>Each community is labelled with the number of stocks, and the pie chart represents the relative composition of each community based on the industry sectors of the constituent stocks (colour legend in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133679#pone.0133679.t001" target="_blank">Table 1</a>). The link weights are negative, indicating that the communities are all residually anti-correlated.</p
The eigenvalue density distribution (of the cross-correlation matrix) for the different indexes, where the upper panels are for the weighted series and the lower panels are for the binary series.
<p>The red curve is the empirical eigenvalue distribution and the blue curve the Marchenko-Pastur distribution. The largest empirical eigenvalue <i>λ</i><sub><i>m</i></sub> is not shown in the plots, but the its value is reported in each panel.</p
The variation of information between the binary and weighted partitions for a sliding window of 600 trading days (approximately 28 moths) starting at Q3 2001.
<p>The VI is measured between the frequent partitions for the different algorithms: Potts (blue), Louvain(red) and Spectral (green).</p
The 10 industry sectors in the Global Industry Classification Standard (GICS), with the color representation used to highlight the sectors in the following Figures.
<p>The 10 industry sectors in the Global Industry Classification Standard (GICS), with the color representation used to highlight the sectors in the following Figures.</p
‘Weighted’ (left) versus ‘Binary’ (right) time series of log-returns of the Apple stock over a period of 40 days starting from 7/5/2011.
<p>‘Weighted’ (left) versus ‘Binary’ (right) time series of log-returns of the Apple stock over a period of 40 days starting from 7/5/2011.</p
The eigenvalue density distribution of the Pearson correlation matrices where the upper panels are for the weighted series and the lower panels are for the binary series.
<p>The red curve is the empirical eigenvalue distribution and the blue curve the Marchenko-Pastur distribution.</p