Search results for " Probability"
showing 10 items of 2176 documents
Kullback-Leibler distance as a measure of the information filtered from multivariate data
2007
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to s…
How does the market react to your order flow?
2012
We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contributions coming from different market participants and study how their behaviour is interconnected. We find evidence that (1) brokers are very heterogeneous in liquidity provision -- some are consistently liquidity providers while others are consistently liquidity takers. (2) The behaviour of brokers is strongly conditioned on the actions of {\it other} brokers. In contrast brokers are only weakly influenced by the impact of their own previous ord…
Spanning Trees and bootstrap reliability estimation in correlation based networks
2007
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 …
Economic Sector Identification in a Set of Stocks Traded at the New York Stock Exchange: A Comparative Analysis
2006
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 th…
Shrinkage and spectral filtering of correlation matrices: A comparison via the Kullback-Leibler distance
2007
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a multivariate Gaussian distribution. Here we use the Kullback-Leibler distance to investigate the performance of filtering methods based on Random Matrix Theory and on the shrinkage technique. We also present some results on the application of the Kullback-Leibler distance to multivariate data which are non Gaussian distributed.
Correlation based networks of equity returns sampled at different time horizons
2006
We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001-2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally filtered graphs generated by sampling the returns at different time horizons ranging from 5 min up to one trading day. This analysis confirms that the selected stocks compose a hierarchical system progressively structuring as the sampling time horizon increases. Finally, a cluster formation, associated to economic sectors, is quantitatively investigated.
A method for approximating optimal statistical significances with machine-learned likelihoods
2022
The European physical journal / C 82(11), 993 (2022). doi:10.1140/epjc/s10052-022-10944-3
$\texttt{HEPfit}$: a Code for the Combination of Indirect and Direct Constraints on High Energy Physics Models
2020
The European physical journal / C Particles and fields C80(5), 456 (2020). doi:10.1140/epjc/s10052-020-7904-z
Numerical Solution of Fuzzy Differential Equations with Z-numbers using Fuzzy Sumudu Transforms
2018
The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of Z-numbers. Important theorems are laid down to illustrate the properties of FST. The theoretical analysis and simulation results show that this new technique is effective to estimate the solutions of FDEs.
First Flight Escape Probability and Uncollided Flux of Nuclear Particles in Convex Bodies with Spherical Symmetry
2016
This paper deals with the evaluation of the first flight escape probability of nuclear particles from convex bodies with spherical symmetry by means of some geometrical arguments and very simple probability considerations. The cases of a full sphere, a one-region spherical shell with an empty central zone, a spherical shell region containing a black central zone, and a full sphere with a sourceless shell have been considered. In all the aforementioned cases, a homogeneous medium and uniform isotropic source have been taken into account. Moreover, a simple and general formula has been derived for the calculation of the uncollided flux that is presupposed to be valid for arbitrary geometries.…