589 research outputs found
Correlation, hierarchies, and networks in financial markets
We discuss some methods to quantitatively investigate the properties of
correlation matrices. Correlation matrices play an important role in portfolio
optimization and in several other quantitative descriptions of asset price
dynamics in financial markets. Specifically, we discuss how to define and
obtain hierarchical trees, correlation based trees and networks from a
correlation matrix. The hierarchical clustering and other procedures performed
on the correlation matrix to detect statistically reliable aspects of the
correlation matrix are seen as filtering procedures of the correlation matrix.
We also discuss a method to associate a hierarchically nested factor model to a
hierarchical tree obtained from a correlation matrix. The information retained
in filtering procedures and its stability with respect to statistical
fluctuations is quantified by using the Kullback-Leibler distance.Comment: 37 pages, 9 figures, 3 table
Profile and challenges of interdisciplinary physics
We discuss profile and challenges of interdisciplinary physics. We start discussing the current definition of physics. We therefore focus on the type of experimental settings observed in different branches of physics. We recall how the term predictability has changed over the last century and we comment on the effects of data deluge in science and society. Lastly we present a few examples of current profile and challenges of interdisciplinary physics
On the interplay between multiscaling and stocks dependence
We find a nonlinear dependence between an indicator of the degree of
multiscaling of log-price time series of a stock and the average correlation of
the stock with respect to the other stocks traded in the same market. This
result is a robust stylized fact holding for different financial markets. We
investigate this result conditional on the stocks' capitalization and on the
kurtosis of stocks' log-returns in order to search for possible confounding
effects. We show that a linear dependence with the logarithm of the
capitalization and the logarithm of kurtosis does not explain the observed
stylized fact, which we interpret as being originated from a deeper
relationship.Comment: 19 pages, 8 figures, 9 table
Profile and challenges of interdisciplinary physics
We discuss profile and challenges of interdisciplinary physics. We start discussing the current definition of physics. We therefore focus on the type of experimental settings observed in different branches of physics. We recall how the term predictability has changed over the last century and we comment on the effects of data deluge in science and society. Lastly we present a few examples of current profile and challenges of interdisciplinary physics
A model for correlations in stock markets
We propose a group model for correlations in stock markets. In the group
model the markets are composed of several groups, within which the stock price
fluctuations are correlated. The spectral properties of empirical correlation
matrices reported in [Phys. Rev. Lett. {\bf 83}, 1467 (1999); Phys. Rev. Lett.
{\bf 83}, 1471 (1999.)] are well understood from the model. It provides the
connection between the spectral properties of the empirical correlation matrix
and the structure of correlations in stock markets.Comment: two pages including one EPS file for a figur
Spanning Trees and bootstrap reliability estimation in correlation based networks
We introduce a new technique to associate a spanning tree to the average
linkage cluster analysis. We term this tree as the Average Linkage Minimum
Spanning Tree. We also introduce a technique to associate a value of
reliability to links of correlation based graphs by using bootstrap replicas of
data. Both techniques are applied to the portfolio of the 300 most capitalized
stocks traded at New York Stock Exchange during the time period 2001-2003. We
show that the Average Linkage Minimum Spanning Tree recognizes economic sectors
and sub-sectors as communities in the network slightly better than the Minimum
Spanning Tree does. We also show that the average reliability of links in the
Minimum Spanning Tree is slightly greater than the average reliability of links
in the Average Linkage Minimum Spanning Tree.Comment: 17 pages, 3 figure
Correlation filtering in financial time series
We apply a method to filter relevant information from the correlation
coefficient matrix by extracting a network of relevant interactions. This
method succeeds to generate networks with the same hierarchical structure of
the Minimum Spanning Tree but containing a larger amount of links resulting in
a richer network topology allowing loops and cliques. In Tumminello et al.
\cite{TumminielloPNAS05}, we have shown that this method, applied to a
financial portfolio of 100 stocks in the USA equity markets, is pretty
efficient in filtering relevant information about the clustering of the system
and its hierarchical structure both on the whole system and within each
cluster. In particular, we have found that triangular loops and 4 element
cliques have important and significant relations with the market structure and
properties. Here we apply this filtering procedure to the analysis of
correlation in two different kind of interest rate time series (16 Eurodollars
and 34 US interest rates).Comment: 10 pages 7 figure
Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
We study the persistence phenomenon in a socio-econo dynamics model using
computer simulations at a finite temperature on hypercubic lattices in
dimensions up to 5. The model includes a ` social\rq local field which contains
the magnetization at time . The nearest neighbour quenched interactions are
drawn from a binary distribution which is a function of the bond concentration,
. The decay of the persistence probability in the model depends on both the
spatial dimension and . We find no evidence of ` blocking\rq in this model.
We also discuss the implications of our results for possible applications in
the social and economic fields. It is suggested that the absence, or otherwise,
of blocking could be used as a criterion to decide on the validity of a given
model in different scenarios.Comment: 11 pages, 4 figure
Economic sector identification in a set of stocks traded at the New York Stock Exchange: a comparative analysis
We review some methods recently used in the literature to detect the
existence of a certain degree of common behavior of stock returns belonging to
the same economic sector. Specifically, we discuss methods based on random
matrix theory and hierarchical clustering techniques. We apply these methods to
a set of stocks traded at the New York Stock Exchange. The investigated time
series are recorded at a daily time horizon.
All the considered methods are able to detect economic information and the
presence of clusters characterized by the economic sector of stocks. However,
different methodologies provide different information about the considered set.
Our comparative analysis suggests that the application of just a single method
could not be able to extract all the economic information present in the
correlation coefficient matrix of a set of stocks.Comment: 13 pages, 8 figures, 2 Table
Networks of equities in financial markets
We review the recent approach of correlation based networks of financial
equities. We investigate portfolio of stocks at different time horizons,
financial indices and volatility time series and we show that meaningful
economic information can be extracted from noise dressed correlation matrices.
We show that the method can be used to falsify widespread market models by
directly comparing the topological properties of networks of real and
artificial markets.Comment: 9 pages, 8 figures. Accepted for publication in EPJ
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