English
Related papers

Related papers: Structure of continuous-time ARMA process driven b…

200 papers

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…

Probability · Mathematics 2023-06-19 Fred Espen Benth , Sven Karbach

The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…

Methodology · Statistics 2023-07-26 Lorenzo Lucchese , Mikko S. Pakkanen , Almut E. D. Veraart

In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling…

Statistics Theory · Mathematics 2022-09-16 Vicky Fasen-Hartmann , Celeste Mayer

We consider a L\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample…

Probability · Mathematics 2018-04-09 Dirk-Philip Brandes , Imma Valentina Curato

In this paper we introduce the Kumaraswamy autoregressive moving average models (KARMA), which is a dynamic class of models for time series taking values in the double bounded interval $(a,b)$ following the Kumaraswamy distribution. The…

Methodology · Statistics 2023-01-16 Fábio Mariano Bayer , Débora Missio Bayer , Guilherme Pumi

This paper considers a continuous time analogue of the classical autoregressive moving average processes, L\'evy-driven CARMA processes. First we describe limiting properties of the periodogram by means of the so-called truncated Fourier…

Probability · Mathematics 2016-08-16 Robert Stelzer , Żywilla fechner

In this paper we discuss dynamic ARMA-type regression models for time series taking values in $(0,\infty)$. In the proposed model, the conditional mean is modeled by a dynamic structure containing autoregressive and moving average terms,…

In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The…

Computation · Statistics 2016-09-09 Javier E. Contreras-Reyes , Wilfredo Palma

We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is…

Probability · Mathematics 2021-04-29 Annemarie Bitter , Robert Stelzer , Bennet Ströh

The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and…

Statistics Theory · Mathematics 2019-05-23 Muneya Matsui

Two-dimensional (2-D) autoregressive moving average (ARMA) models are commonly applied to describe real-world image data, usually assuming Gaussian or symmetric noise. However, real-world data often present non-Gaussian signals, with…

Methodology · Statistics 2022-08-09 B. G. Palm , F. M. Bayer , R. J. Cintra

Periodicity is a common feature of time series. For finite-dimensional data, periodic autoregressive moving average (ARMA) models have been extensively studied. In functional time series analysis, AR models have been extended to incorporate…

Methodology · Statistics 2025-12-18 Sebastian Kühnert , Juhyun Park

The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear coefficients driven by a class of L\'evy processes is investigated. The dependence of the convergence order of the…

Numerical Analysis · Mathematics 2023-11-21 Xiaotong Li , Wei Liu , Hongjiong Tian

In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form $$Z_{t} = \int_{\mathbb{R}}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}$$ with a deterministic kernel (\K\) and a…

Statistics Theory · Mathematics 2016-08-19 Denis Belomestny , Vladimir Panov , Jeannette Woerner

Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…

Probability · Mathematics 2022-04-20 G. L. Feltes , S. R. C. Lopes

Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification…

Systems and Control · Electrical Eng. & Systems 2022-12-01 Alex Nguyen-Le , Victor M. Preciado

In this paper we define and characterize cointegrated continuous-time linear state-space models. A main result is that a cointegrated continuous-time linear state-space model can be represented as a sum of a L\'evy process and a stationary…

Probability · Mathematics 2018-01-03 Vicky Fasen-Hartmann , Markus Scholz

One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time…

Methodology · Statistics 2021-05-13 Tingguo Zheng , Han Xiao , Rong Chen

This paper proposes the quantile unit-log-symmetric autoregressive moving average (QULS--ARMA) model for bounded time series on the open unit interval $(0,1)$. The model extends the unit-log-symmetric family by introducing a quantile-based…

Computation · Statistics 2026-05-26 Helton Saulo , Roberto Vila , Filidor Vilca

In this paper, we propose a novel variable selection approach in the framework of sparse high-dimensional GLARMA models. It consists in combining the estimation of the autoregressive moving average (ARMA) coefficients of these models with…

Statistics Theory · Mathematics 2019-10-14 Céline Lévy-Leduc , Sarah Ouadah , Laure Sansonnet