Related papers: The multivariate ARMA/CARMA transformation relatio…
We propose a parametrization of autoregressive unit roots ARMA models (ARUMA) with partial autocorrelation coefficients to specify the autoregressive and integrated part of the model. We obtain the algebraic properties of the partial…
We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed with an invariant measure. We add some criteria, theoretical…
An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the…
We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a…
Continuous-time autoregressive and moving average (CARMA) models are extensively used to model high-frequency and irregularly sampled data. We study Whittle estimation for the model parameters when the process is observed at renewal times.…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
We establish several closed pricing formula for various path-independent payoffs, under an exponential L\'evy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools…
We propose a continuous model for evolutionary rate variation across sites and over the tree and derive exact transition probabilities under this model. Changes in rate are modelled using the CIR process, a diffusion widely used in…
Time-dependent light-matter interactions are a widespread means by which to describe controllable experimental operations. They can be viewed as an approximation in which a third system - the control system - is treated as external within…
We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…
Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
In this paper we present a robust estimator for the parameters of a continuous-time ARMA(p,q) (CARMA(p,q)) process sampled equidistantly which is not necessarily Gaussian. Therefore, an indirect estimation procedure is used. It is an…
Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…
The problem of approximating/tracking the value of a Wiener process is considered. The discretization points are placed at times when the value of the process differs from the approximation by some amount, here denoted by eta. It is found…
We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of…