Related papers: Empirical spectral processes for stationary state …
We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is…
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…
We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the…
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate L\'evy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting…
In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, we introduce matrix-valued MCARMA processes with L\'evy noise and present necessary and…
In this note we show that the locally stationary wavelet process can be decomposed into a sum of signals, each of which following a moving average process with time-varying parameters. We then show that such moving average processes are…
We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…
We estimate the kernel function of a symmetric alpha stable ($S\alpha S$) moving average random function which is observed on a regular grid of points. The proposed estimator relies on the empirical normalized (smoothed) periodogram. It is…
We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Levy processes in Hilbert space. We provide the basic definitions, show relevant…
The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the $\alpha$-stable locally stationary process by modifying the innovations…
In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…
This paper aims at semi-parametrically estimating the input process to a L\'evy-driven queue by sampling the workload process at Poisson times. We construct a method-of-moments based estimator for the L\'evy process' characteristic…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. In particular a conditionally…
We consider high frequency samples from ergodic L\'evy driven stochastic differential equation (SDE) with drift coefficient $a(x,\alpha)$ and scale coefficient $c(x,\gamma)$ involving unknown parameters $\alpha$ and $\gamma$. We suppose…
In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…
The Mat\'ern covariance model is ubiquitous in spatial modelling, but there is no default choice for spatio-temporal modelling. In this paper, we consider the recently proposed ``diffusion-based'' extension of the spatial Mat\'ern…
In this article, we propose a spectral method for a class of multivariate inhomogeneous spatial point processes, namely the second-order intensity reweighted stationary processes. A key ingredient of our approach is utilizing the asymptotic…
In this paper, using spectral theory of Hilbertian operators, we study ARMA Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their…
We introduce L\'evy-driven causal CARMA random fields on $\mathbb{R}^d$, extending the class of CARMA processes. The definition is based on a system of stochastic partial differential equations which generalize the classical state-space…