Emanuele Taufer

Testing exponentiality by comparing the empirical distribution function of the normalized spacings with that of the original data

We introduce new goodness of fit tests for exponentiality by using a characterization based on normalized spacings. We provide relevant asymptotic theory for these tests and study their efficiency. An empirical power study and comparisons are also provided.

Simulation of Lévy-driven Ornstein-Uhlenbeck processes with given marginal distribution

A simulation procedure for obtaining discretely observed values of Ornstein-Uhlenbeck processes with given (self-decomposable) marginal distribution is provided. The method proposed, based on inversion of the characteristic function, completely circumvents the problems encountered when trying to reproduce small jumps of Levy processes. Error bounds for the proposed procedure are provided and its performance is numerically assessed.

Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models

Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. A characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models is proposed. Explicit expressions of the characteristic functions for various cases of interest are derived. The asymptotic properties of the estimators are analyzed and their small-sample performance is evaluated by means of a simulation experiment. Finally, two real-data applications show that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.

Use of mean residual life in testing departures from exponentiality

We utilize the important characterization that E(X−t|X>t) is a constant for t∈[0, ∞) if and only if X is distributed as an exponential random variable, in order to construct a new test procedure for exponentiality. We discuss asymptotic distribution theory and other properties of the proposed procedure. Simulation studies indicate that the proposed statistic has very good power in a large variety of situations.

Convergence of integrated superpositions of Ornstein-Uhlenbeck processes to fractional Brownian motion

Superpositions of Ornstein-Uhlenbeck processes provide convenient ways to build stationary processes with given marginal distributions and long range dependence. After reviewing some of the basic features, we present several examples of processes with non-Gaussian marginal distributions. Our main results concern asymptotic properties of sums and partial sums of these processes and their polynomial functions. Further, we discuss some applications to estimation.

ON ENTROPY BASED TESTS FOR EXPONENTIALITY

ABSTRACT Recent literature has proposed a test for exponentiality based on sample entropy. We consider transformations of the observations which turn the test of exponentiality into one of uniformity and use a corresponding test based on entropy. The test based on the transformed variables performs better in many cases of interest.

Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function

We consider goodness-of-fit testing for multivariate stable distributions. The proposed test statistics exploit a characterizing property of the characteristic function of these distributions and are consistent under some conditions. The asymptotic distribution is derived under the null hypothesis as well as under local alternatives. Conditions for an asymptotic null distribution free of parameters and for affine invariance are provided. Computational issues are discussed in detail and simulations show that with proper choice of the user parameters involved, the new tests lead to powerful omnibus procedures for the problem at hand.

Simulation of multifractal products of Ornstein-Uhlenbeck type processes

This paper investigates and provides evidence of the multifractal properties of products of the exponential of Ornstein–Uhlenbeck processes driven by Levy motion. We demonstrate in detail the construction of a multifractal process with gamma subordinator as the background driving Levy process. Simulations are performed for the scenarios corresponding to the normal inverse Gaussian, gamma and inverse Gaussian distributions. The log periodograms and Renyi functions of the simulated processes are also computed to investigate their multifractality.

Asymptotic properties of the partition function and applications in tail index inference of heavy-tailed data

The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution underlying the data both in independent identically distributed and weakly dependent cases. These results will be used to develop graphical and estimation methods for the tail index of a distribution. The performance of the tools proposed is analysed and compared with other methods by means of simulations and examples.

On the empirical process of strongly dependent stable random variables: asymptotic properties, simulation and applications

This paper analyzes the limit properties of the empirical process of α-stable random variables with long range dependence. The α-stable random variables are constructed by nonlinear transformations of bivariate sequences of strongly dependent gaussian processes. The approach followed allows an analysis of the empirical process by means of expansions in terms of bivariate Hermite polynomials for the full range 0 < α < 2. A weak uniform reduction principle is provided and it is shown that the limiting process is gaussian. The results of the paper different substantailly from those available for empirical processes obtained by stable moving averages with long memory. An application to goodness-of-fit testing is discussed.