Related papers: A comparison of Hurst exponent estimators in long-…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We show weak convergence of the time-$t$ marginals for the integrated variance in a re-scaled rough Heston model to an Inverse Gaussian L\'{e}vy process. This shows we can obtain such a limit without having to impose that the true Hurst…
We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly…
In this paper, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which one performs best to identify the transition from random efficient market behavior (EM) to herding behavior…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…
We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…
We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt…
The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global…
We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index…
Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…
Complex systems often involve random fluctuations for which self-similar properties in space and time play an important role. Fractional Brownian motions, characterized by a single scaling exponent, the Hurst exponent $H$, provide a…
We investigate long and short memory in $\alpha$-stable moving averages and max-stable processes with $\alpha$-Fr\'echet marginal distributions. As these processes are heavy-tailed, we rely on the notion of long range dependence suggested…