Ornstein-Uhlenbeck type processes with heavy distribution tails

  title={Ornstein-Uhlenbeck type processes with heavy distribution tails},
  author={Konstantin Borovkov and Geoffrey Decrouez},
  journal={arXiv: Probability},
We consider a transformed Ornstein-Uhlenbeck process model that can be a good candidate for modelling real-life processes characterized by a combination of time-reverting behaviour with heavy distribution tails. We begin with presenting the results of an exploratory statistical analysis of the log prices of a major Australian public company, demonstrating several key features typical of such time series. Motivated by these findings, we suggest a simple transformed Ornstein-Uhlenbeck process… 

Figures and Tables from this paper

Main statistical features for building a pedestrian mobility model
The GPS data set of a collection of 260 students from up to 10 schools in the Barcelona Metropolitan Area is studied, providing a first analysis to very valuable data to model pedestrian mobility with specific origin-destination journeys.


Ornstein-Uhlenbeck type processes with non-normal distribution
We analyse a class of diffusion models that (i) allows an explicit expression for the likelihood function of discrete time observation, (ii) allows the possibility of heavy-tailed observations, and
On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process
We prove the following probabilistic properties of a multidimensional Ornstein-Uhlenbeck process driven by a general Levy process, under mild regularity conditions: the strong Feller property; the
First-passage-time density and moments of the Ornstein-Uhlenbeck process
A detailed study of the asymptotic behavior of the first-passage-time p.d.f. and its moments is carried out for an unrestricted conditional Ornstein-Uhlenbeck process and for a constant boundary.
Tail and Quantile Estimation for Strongly Mixing Stationary Sequences
Abstract : This paper primarily concerns the estimation of tail parameters for the marginal distribution F of the terms of a strongly mixing stationary sequence when 1-F(t) decreases exponentially,
A practical guide to heavy tails: statistical techniques and applications
Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al
A hyperbolic diffusion model for stock prices
A model for stock prices which is a generalization of the model behind the Black–Scholes formula for pricing European call options is considered and a simple general way of constructing a zero-drift diffusion with a given marginal distribution is introduced.
A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems
The study of the finite-sample performance of the multiplier version of the goodness-of-fit test for bivariate one-parameter copulas showed that it provides a valid alternative to the parametric bootstrap-based test while being orders of magnitude faster.
Handbook of heavy tailed distributions in finance
Preface (S.T. Rachev). Heavy Tails in Finance for Independent or Multifractal Price Increments (B. Mandelbrot). Financial Risk and Heavy Tails (B. Bradley, M. Taqqu). Modelling Financial Data with
Statistics of random processes
1. Essentials of Probability Theory and Mathematical Statistics.- 2. Martingales and Related Processes: Discrete Time.- 3. Martingales and Related Processes: Continuous Time.- 4. The Wiener Process,
Modeling Multivariate Distributions with Continuous Margins Using the copula R Package
The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual