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Waiting-times and returns in high-frequency financial data: an empirical study

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In this paper, the statistical properties of General Electric stock prices, traded at NYSE, in October 1999, are critically revised in the framework of theoretical predictions based on a continuous-time random walk model.
Abstract
In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock prices, traded at NYSE, in October 1999. These properties are critically revised in the framework of theoretical predictions based on a continuous-time random walk model.

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Journal ArticleDOI

The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.
Journal ArticleDOI

Finite difference approximations for fractional advection-dispersion flow equations

TL;DR: In this paper, the authors developed practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain and demonstrated the practical application of these results is illustrated by modeling a radial flow problem.
Book ChapterDOI

Multi-index Mittag-Leffler Functions

TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
Journal ArticleDOI

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

TL;DR: In this article, the Riesz fractional diffusion equation (RFDE) and RFADE (RFADE) were considered and analytic solutions of both the RFDE and the RFADE were derived.
Journal ArticleDOI

Finite difference methods for two-dimensional fractional dispersion equation

TL;DR: In this article, a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equations with variable coefficients on a finite domain is discussed.
References
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Journal ArticleDOI

Higher Transcendental Functions

Thomas M. Macrobert
- 01 Feb 1955 - 
TL;DR: Higher Transcendental Functions Based on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project as discussed by the authors, are presented in Table 1.
Journal ArticleDOI

A subordinated stochastic process model with finite variance for speculative prices

Peter King Clark
- 01 Jan 1973 - 
TL;DR: In this article, a general class of finite-variance distributions for price changes is described, and a member of this class, the lognormal-normal, is tested against previously proposed distributions for speculative price differences.
Book

Introduction to Econophysics: Correlations and Complexity in Finance

TL;DR: Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.
Book

Digital spectral analysis : with applications

S L Marple
TL;DR: This new book provides a broad perspective of spectral estimation techniques and their implementation concerned with spectral estimation of discretespace sequences derived by sampling continuousspace signals.