641 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
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
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
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
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
Sector identification in a set of stock return time series traded at the London Stock Exchange
We compare 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 portfolio of stocks traded at the London Stock Exchange. The investigated
time series are recorded both at a daily time horizon and at a 5-minute time
horizon. The correlation coefficient matrix is very different at different time
horizons confirming that more structured correlation coefficient matrices are
observed for long time horizons. All the considered methods are able to detect
economic information and the presence of clusters characterized by the economic
sector of stocks. However different methods present a different degree of
sensitivity with respect to different sectors. 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 stock portfolio.Comment: 28 pages, 13 figures, 3 Tables. Proceedings of the conference on
"Applications of Random Matrices to Economy and other Complex Systems",
Krakow (Poland), May 25-28 2005. Submitted for pubblication to Acta Phys. Po
Value-at-Risk and Tsallis statistics: risk analysis of the aerospace sector
In this study, we analyze the aerospace stocks prices in order to
characterize the sector behavior. The data analyzed cover the period from
January 1987 to April 1999. We present a new index for the aerospace sector and
we investigate the statistical characteristics of this index. Our results show
that this index is well described by Tsallis distribution. We explore this
result and modify the standard Value-at-Risk (VaR), financial risk assessment
methodology in order to reflect an asset which obeys Tsallis non-extensive
statistics.Comment: 10 pages, 4 figures, 1 table, to appear in Physica
Data clustering and noise undressing for correlation matrices
We discuss a new approach to data clustering. We find that maximum likelihood
leads naturally to an Hamiltonian of Potts variables which depends on the
correlation matrix and whose low temperature behavior describes the correlation
structure of the data. For random, uncorrelated data sets no correlation
structure emerges. On the other hand for data sets with a built-in cluster
structure, the method is able to detect and recover efficiently that structure.
Finally we apply the method to financial time series, where the low temperature
behavior reveals a non trivial clustering.Comment: 8 pages, 5 figures, completely rewritten and enlarged version of
cond-mat/0003241. Submitted to Phys. Rev.
Evidence of discrete scale invariance in DLA and time-to-failure by canonical averaging
Discrete scale invariance, which corresponds to a partial breaking of the
scaling symmetry, is reflected in the existence of a hierarchy of
characteristic scales l0, c l0, c^2 l0,... where c is a preferred scaling ratio
and l0 a microscopic cut-off. Signatures of discrete scale invariance have
recently been found in a variety of systems ranging from rupture, earthquakes,
Laplacian growth phenomena, ``animals'' in percolation to financial market
crashes. We believe it to be a quite general, albeit subtle phenomenon. Indeed,
the practical problem in uncovering an underlying discrete scale invariance is
that standard ensemble averaging procedures destroy it as if it was pure noise.
This is due to the fact, that while c only depends on the underlying physics,
l0 on the contrary is realisation-dependent. Here, we adapt and implement a
novel so-called ``canonical'' averaging scheme which re-sets the l0 of
different realizations to approximately the same value. The method is based on
the determination of a realization-dependent effective critical point obtained
from, e.g., a maximum susceptibility criterion. We demonstrate the method on
diffusion limited aggregation and a model of rupture.Comment: 14 pages, 6 figures, in press in Int. J. Mod. Phys.
Methods for measuring the citations and productivity of scientists across time and discipline
Publication statistics are ubiquitous in the ratings of scientific
achievement, with citation counts and paper tallies factoring into an
individual's consideration for postdoctoral positions, junior faculty, tenure,
and even visa status for international scientists. Citation statistics are
designed to quantify individual career achievement, both at the level of a
single publication, and over an individual's entire career. While some academic
careers are defined by a few significant papers (possibly out of many), other
academic careers are defined by the cumulative contribution made by the
author's publications to the body of science. Several metrics have been
formulated to quantify an individual's publication career, yet none of these
metrics account for the dependence of citation counts and journal size on time.
In this paper, we normalize publication metrics across both time and discipline
in order to achieve a universal framework for analyzing and comparing
scientific achievement. We study the publication careers of individual authors
over the 50-year period 1958-2008 within six high-impact journals: CELL, the
New England Journal of Medicine (NEJM), Nature, the Proceedings of the National
Academy of Science (PNAS), Physical Review Letters (PRL), and Science. In
comparing the achievement of authors within each journal, we uncover
quantifiable statistical regularity in the probability density function (pdf)
of scientific achievement across both time and discipline. The universal
distribution of career success within these arenas for publication raises the
possibility that a fundamental driving force underlying scientific achievement
is the competitive nature of scientific advancement.Comment: 25 pages in 1 Column Preprint format, 7 Figures, 4 Tables. Version
II: changes made in response to referee comments. Note: change in definition
of "Paper shares.
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