arXiv subjects

H. F. Coronel-Brizio

Publications and source records attributed to H. F. Coronel-Brizio.

12 recordsLinked to original sources

arXiv2019

A multi-scale symmetry analysis of uninterrupted trends returns of daily financial indices

We present a symmetry analysis of the distribution of variations of different financial indices, by means of a statistical procedure developed by the authors based on a symmetry statistic by Einmahl and Mckeague. We applied this statistical methodology to financial uninterrupted daily trends returns and to other derived observable. In our opinion, to study distributional symmetry, trends returns offer more advantages than the commonly used daily financial returns; the two most important being: 1) Trends returns involve sampling over different time scales and 2) By construction, this variable time series contains practically the same number of non-negative and negative entry values. We also show that these time multi-scale returns display distributional bi-modality. Daily financial indices analyzed in this work, are the Mexican IPC, the American DJIA, DAX from Germany and the Japanese Market index Nikkei, covering a time period from 11-08-1991 to 06-30-2017. We show that, at the time scale resolution and significance considered in this paper, it is almost always feasible to find an interval of possible symmetry points containing one most plausible symmetry point denoted by C. Finally, we study the temporal evolution of C showing that this point is seldom zero and responds with sensitivity to extreme market events.

q-fin.ST↗

arXiv2014

Wealth distribution of simple exchange models coupled with extremal dynamics

Punctuated Equilibrium (PE) states that after long periods of evolutionary quiescence, species evolution can take place in short time intervals, where sudden differentiation makes new species emerge and some species extinct. In this paper, we introduce and study the effect of punctuated equilibrium on two different asset exchange models: The yard sale model (YS, winner gets a random fraction of a poorer player's wealth) and the theft and fraud model (TF, winner gets a random fraction of the loser's wealth). The resulting wealth distribution is characterized using the Gini index. In order to do this, we consider PE as a perturbation with probability $ρ$ of being applied. We compare the resulting values of the Gini index at different increasing values of $ρ$ in both models. We found that in the case of the TF model, the Gini index reduces as the perturbation $ρ$ increases, not showing dependence with the agents number. While for YS we observe a phase transition which happens around $ρ_c=0.79$. For perturbations $ρ<ρ_c$ the Gini index reaches the value of one as time increases (an extreme wealth condensation state), whereas for perturbations bigger or equal than $ρ_c$ the Gini index becomes different to one, avoiding the system reaches this extreme state. We show that both simple exchange models coupled with PE dynamics give more realistic results. In particular for YS, we observe a power low decay of wealth distribution.

physics.soc-ph↗

arXiv2012

Analysis of short term price trends in daily stock-market index data

In financial time series there are periods in which the value increases or decreases monotonically. We call those periods elemental trends and study the probability distribution of their duration for the indices DJIA, NASDAQ and IPC. It is found that the trend duration distribution often differs from the one expected under no memory. The expected and observed distributions are compared by means of the Anderson-Darling test.

q-fin.ST↗

arXiv2010

The Anderson-Darling test of fit for the power law distribution from left censored samples

Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum likelihood estimators and tables of asymptotic percentage points for the A^2 statistic are given. The technique is illustrated for data from the Dow Jones Industrial Average index, an example of high theoretical and practical importance in Econophysics, Finance, Physics, Biology and, in general, in other related Sciences such as Complexity Sciences.

physics.data-an↗

arXiv2008

Statistical auditing and randomness test of lotto k/N-type games

One of the most popular lottery games worldwide is the so-called ``lotto k/N''. It considers N numbers 1,2,...,N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.

physics.data-an↗

arXiv2007

Stylized Facts Generated Through Cellular Automata Models. Case of Study: The Game of Life

In the present work, a geometrical method to generate a two dimensional random walk by means of a bidimensional Cellular Automaton is presented. We illustrate it by means of Conway's Game of Life with periodical borders, with a large lattice of 3000 x 3000 cells. The obtained random walk is of character anomalous, and its projection to a one dimensional random walk is analyzed, showing that it presents some statistical properties similar to the so-called stylized facts observed in financial time series. We consider that the procedure presented here is important not only because of its simplicity, but also because it could help us to understand and shed light on the stylized facts formation mechanism.

physics.comp-ph↗

arXiv2007

Assessing symmetry of financial returns series

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic Tn for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic Tn are also calculated and a procedure for assessing symmetry for the analysis of the returns of stock market indices is presented.

physics.data-an↗

arXiv2006

Una prueba empirica de generadores de numeros pseudoaleatorios mediante un proceso de decaimiento exponencial

Empirical tests for pseudorandom number generators based on the use of processes or physical models have been successfuly used and are considered as complementary to theoretical test of randomness. In this work a statistical methodology for evaluating the quality of pseudorandom number generators is presented. The method is illustrated in the context of the so-called exponential decay process, using some pseudorandom number generators commonly used in physics.

physics.comp-ph↗

arXiv2006

Evidence of Increment of Efficiency of the Mexican Stock Market Through the Analysis of its Variations

It is well known that there exist statistical and structural differences between the stock markets of developed and emerging countries. In this work, we present an analysis of the variations and autocorrelations of the Mexican Stock Market index (IPC) for different periods of its historical daily data, showing evidence that the Mexican Stock Market has been increasing its efficiency in recent times. We have analyzed the returns autocorrelation function (ACF) and used detrended fluctuation analysis (DFA) methods. We also analyze the volatility of the IPC and the Dow Jones Industrial Average (DJIA) and compare their evolution. The data samples analyzed here, correspond to daily values of the IPC and DJIA for the period 10/30/1978 to 02/28/2006.

physics.soc-ph↗

arXiv2004

On fitting the Pareto-Levy distribution to stock market index data: selecting a suitable cutoff value

The so-called Pareto-Levy or power-law distribution has been successfully used as a model to describe probabilities associated to extreme variations of worldwide stock markets indexes data and it has the form $Pr(X>x) ~ x**(-alpha) for gamma< x <infinity. The selection of the threshold parameter gamma$ from empirical data and consequently, the determination of the exponent alpha, is often is done by using a simple graphical method based on a log-log scale, where a power-law probability plot shows a straight line with slope equal to the exponent of the power-law distribution. This procedure can be considered subjective, particularly with regard to the choice of the threshold or cutoff parameter gamma. In this work is presented a more objective procedure, based on a statistical measure of discrepancy between the empirical and the Pareto-Levy distribution. The technique is illustrated for data sets from the New York Stock Exchange Index and the Mexican Stock Market Index (IPC).

cond-mat.other↗

arXiv2004

Asymptotic behavior of the Daily Increment Distribution of the IPC, the Mexican Stock Market Index

In this work, a statistical analysis of the distribution of daily fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of the IPC covering the 13-year period 04/19/1990 - 08/21/2003 was analyzed and the cumulative probability distribution of its daily logarithmic variations studied. Results showed that the cumulative distribution function for extreme variations, can be described by a Pareto-Levy model with shape parameters alpha=3.634 +- 0.272 and alpha=3.540 +- 0.278 for its positive and negative tails respectively. This result is consistent with previous studies, where it has been found that 2.5< alpha <4 for other financial markets worldwide.

cond-mat.other↗

arXiv2003

Fitting the Power-law Distribution to the Mexican Stock Market index data

In the spirit of the emergent field of econophysics, a goodness-of-fit test for the Power-Law distribution, based on the Empirical Distribution Function (EDF) is presented, and related problems are discussed. An analysis of the tail behaviour of the daily logarithmic variation of the Mexican Stock Market Index (IPC), showed distributional properties which are consistent with previous studies.

cond-mat.stat-mech↗