arXiv subjects

F. Lillo

Publications and source records attributed to F. Lillo.

13 recordsLinked to original sources

arXiv2023

Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems

We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invariant measure of the map, and show that the average Lyapunov exponent depends continuously on the Markov chain parameters. Representing the Markov chain in terms of random transformation enables us to state and prove the Central Limit Theorem, the large deviation principle, and the Berry-Ess\`een inequality. We perform a multifractal analysis for the invariant and the stationary measures, and we prove Gumbel's law for the Markov chain with an extreme index equal to 1. In addition, we present an example linked to the financial concept of systemic risk and leverage cycle, and we use the model to investigate the finite sample properties of our asymptotic results.

math.DS↗

arXiv2022

Measuring price impact and information content of trades in a time-varying setting

We propose a non-linear observation-driven version of the Hasbrouck (1991) model for dynamically estimating trades' market impact and information content. We find that market impact displays an intraday pattern superimposed with large fluctuations. Some of them are exogenous, and, as an example, we investigate market impact dynamics around FOMC announcements. Contrary to Hasbrouck (1991), we find that the information content of trades depends on the local liquidity level and the recent history of prices and trades. Finally, we use the model to estimate the time-varying permanent impact parameter, which allows performing a dynamic transaction cost analysis.

q-fin.TR↗

arXiv2016

Statistical characterization of deviations from planned flight trajectories in air traffic management

Understanding the relation between planned and realized flight trajectories and the determinants of flight deviations is of great importance in air traffic management. In this paper we perform an in depth investigation of the statistical properties of planned and realized air traffic on the German airspace during a 28 day periods, corresponding to an AIRAC cycle. We find that realized trajectories are on average shorter than planned ones and this effect is stronger during night-time than daytime. Flights are more frequently deviated close to the departure airport and at a relatively large angle to destination. Moreover, the probability of a deviation is higher in low traffic phases. All these evidences indicate that deviations are mostly used by controllers to give directs to flights when traffic conditions allow it. Finally we introduce a new metric, termed difork, which is able to characterize navigation points according to the likelihood that a deviation occurs there. Difork allows to identify in a statistically rigorous way navigation point pairs where deviations are more (less) frequent than expected under a null hypothesis of randomness that takes into account the heterogeneity of the navigation points. Such pairs can therefore be seen as sources of flexibility (stability) of controllers traffic management while conjugating safety and efficiency.

physics.soc-ph↗

arXiv2008

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.

q-fin.ST↗

arXiv2008

Generation of hierarchically correlated multivariate symbolic sequences

We introduce an algorithm to generate multivariate series of symbols from a finite alphabet with a given hierarchical structure of similarities. The target hierarchical structure of similarities is arbitrary, for instance the one obtained by some hierarchical clustering procedure as applied to an empirical matrix of Hamming distances. The algorithm can be interpreted as the finite alphabet equivalent of the recently introduced hierarchically nested factor model (M. Tumminello et al. EPL 78 (3) 30006 (2007)). The algorithm is based on a generating mechanism that is different from the one used in the mutation rate approach. We apply the proposed methodology for investigating the relationship between the bootstrap value associated with a node of a phylogeny and the probability of finding that node in the true phylogeny.

physics.comp-ph↗

arXiv2007

Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distance

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.

physics.data-an↗

arXiv2007

Hierarchically nested factor model from multivariate data

We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a factor model, the hierarchically nested factor model. In this model, factors are mutually independent and hierarchically organized. Finally, we use a bootstrap based procedure to reduce the number of factors in the model with the aim of retaining only those factors significantly robust with respect to the statistical uncertainty due to the finite length of data records.

cond-mat.dis-nn↗

arXiv2006

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.

physics.soc-ph↗

arXiv2006

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.

physics.soc-ph↗

arXiv2005

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.

cond-mat.dis-nn↗

arXiv2005

A theory for long-memory in supply and demand

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such large orders is power law distributed, this gives rise to power law decaying autocorrelations in the signs of executed orders. More specifically, we show that if the cumulative distribution of large orders of volume v is proportional to v to the power -alpha and the size of executed orders is constant, the autocorrelation of order signs as a function of the lag tau is asymptotically proportional to tau to the power -(alpha - 1). This is a long-memory process when alpha < 2. With a few caveats, this gives a good match to the data. A version of the model also shows long-memory fluctuations in order execution rates, which may be relevant for explaining the long-memory of price diffusion rates.

cond-mat.other↗

arXiv2004

Inverted Repeats in Viral Genomes

We investigate 738 complete genomes of viruses to detect the presence of short inverted repeats. The number of inverted repeats found is compared with the prediction obtained for a Bernoullian and for a Markovian control model. We find as a statistical regularity that the number of observed inverted repeats is often greater than the one expected in terms of a Bernoullian or Markovian model in several of the viruses and in almost all those with a genome longer than 30,000 bp.

q-bio.QM↗

arXiv2004

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.

cond-mat.stat-mech↗