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In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily…

Statistics Theory · Mathematics 2025-03-06 Yacouba Boubacar Mainassara , Landy Rabehasaina , Armel Bra

We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…

Statistics Theory · Mathematics 2020-03-12 Niko Lietzén , Lauri Viitasaari , Pauliina Ilmonen

We examine the asymptotic behaviour of the sample autocovariance in a continuous-time moving average model with long-range dependence. We show that it is either asymptotically Rosenblatt distributed or stable distributed. This shows that…

Probability · Mathematics 2015-11-24 Felix Spangenberg

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential…

Methodology · Statistics 2020-10-13 Sigrunn H. Sørbye , Pedro G. Nicolau , Håvard Rue

In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and,…

Probability · Mathematics 2023-01-05 Marko Voutilainen , Lauri Viitasaari , Pauliina Ilmonen

Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…

Optimization and Control · Mathematics 2024-02-28 Yufang Cui , Anders Lindquist

We study stationarity and moments properties of some count time series models from contraction and stability properties of iterated random maps. Both univariate and multivariate processes are considered, including the recent multivariate…

Statistics Theory · Mathematics 2019-09-26 Zinsou Max Debaly , Lionel Truquet

This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…

Statistics Theory · Mathematics 2010-11-12 Wilfredo Palma , Ricardo Olea

Estimating the periodicity of a stationary time series via fitting a second order stationary autoregressive (AR(2)) model has been initiated by the seminal paper of Yule(1927).. We investigate properties of this procedure when applied to a…

Statistics Theory · Mathematics 2025-12-01 Jens-Peter Kreiss , Panagiotis Maouris , Efstathios Paparoditis

In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complex-valued Ornstein-Uhlenbeck processes under some mild assumptions. The…

Statistics Theory · Mathematics 2021-02-24 Vicky Fasen-Hartmann , Markus Scholz

In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…

Probability · Mathematics 2023-11-08 Hui Jiang , Guangyu Yang , Mingming Yu

We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…

Statistics Theory · Mathematics 2008-08-12 Sébastien Van Bellegem , Rainer von Sachs

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Probability · Mathematics 2021-04-13 Suryadeepto Nag

We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary,…

Methodology · Statistics 2011-07-27 Emily B. Fox , Mike West

The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior…

Statistics Theory · Mathematics 2015-08-10 Vicky Fasen

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…

Methodology · Statistics 2023-02-15 Shu Wei Chou-Chen , Pedro A. Morettin

This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…

Statistics Theory · Mathematics 2025-03-19 Henry Antonio Palasciano , Marina I. Knight , Guy P. Nason

We study the effect of stochastic sampling on the estimation of the drift parameter of continuous time AR(1) process. A natural distribution free moment estimator is considered for the drift based on stochastically observed time points. The…

Statistics Theory · Mathematics 2013-07-29 Radhendushka Srivastava , Ping Li

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

Statistics Theory · Mathematics 2023-07-10 Alexandre Lecestre

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