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We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

Probability · Mathematics 2024-11-21 Paweł J. Szabłowski

We design a novel, nonlinear single-source-of-error model for analysis of multiple business cycles. The model's specification is intended to capture key empirical characteristics of business cycle data by allowing for simultaneous cycles of…

Methodology · Statistics 2024-06-05 Łukasz Lenart , Łukasz Kwiatkowski , Justyna Wróblewska

In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in…

Information Theory · Computer Science 2017-05-10 Mahdi Barzegar Khalilsarai , Saeid Haghighatshoar , Giuseppe Caire , Gerhard Wunder

By the methods of the time series analysis we investigate human vestibular and optovestibular nystagmus time series. They can be stationary or nonstationary and are between the classes of purely periodic or purely chaotic time series. The…

Chaotic Dynamics · Physics 2007-05-23 Nikolay K. Vitanov , Veneta Todorova

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate…

Stationary quantum stochastic process j is introduced as a *-homomorphism embedding an involutive graded algebra $\tilde K=\oplus_{i=1}^{\infty}K_i$ into a ring of (abelian) cohomologies of the one-parameter group $\alpha$ consisting of…

Functional Analysis · Mathematics 2007-05-23 Grigori G. Amosov

Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also…

Statistics Theory · Mathematics 2008-11-07 P. M. Robinson

We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.

Probability · Mathematics 2016-04-28 Paolo Dai Pra , Pierre-Yves Louis , Sylvie Roelly

For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for…

Statistics Theory · Mathematics 2022-10-11 Jonas Krampe , Suhasini Subba Rao

Time-dependent data often exhibit characteristics, such as non-stationarity and heavy-tailed errors, that would be inappropriate to model with the typical assumptions used in popular models. Thus, more flexible approaches are required to be…

Machine Learning · Statistics 2023-11-02 Taole Sha , Michael Minyi Zhang

We consider strictly stationary stochastic processes of Hilbert space-valued random variables and focus on fully functional tests for the equality of the lag-zero autocovariance operators of several independent functional time series. A…

Statistics Theory · Mathematics 2020-04-07 Dimitrios Pilavakis , Efstathios Paparoditis , Theofanis Sapatinas

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…

Statistics Theory · Mathematics 2024-09-25 Claudia Kirch , Alexander Meier , Renate Meyer , Yifu Tang

We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…

Adaptation and Self-Organizing Systems · Physics 2023-01-19 Norihisa Namura , Shohei Takata , Katsunori Yamaguchi , Ryota Kobayashi , Hiroya Nakao

We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…

Probability · Mathematics 2022-01-17 Benoît Henry , Sylvie Méléard , Viet Chi Tran

Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous…

Let $B=(B_t)_{t\in {\mathbb{R}}}$ be a two-sided standard Brownian motion. An unbiased shift of $B$ is a random time $T$, which is a measurable function of $B$, such that $(B_{T+t}-B_T)_{t\in {\mathbb{R}}}$ is a Brownian motion independent…

Probability · Mathematics 2014-02-26 Günter Last , Peter Mörters , Hermann Thorisson

Existing frequency domain methods for bootstrapping time series have a limited range. Consider for instance the class of spectral mean statistics (also called integrated periodograms) which includes many important statistics in time series…

Methodology · Statistics 2018-06-19 Marco Meyer , Efstathios Paparoditis , Jens-Peter Kreiss

Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…

Mathematical Physics · Physics 2021-03-17 Yu-Chen Cheng , Hong Qian

It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…

Probability · Mathematics 2019-11-19 Anastassia Baxevani , Krzysztof Podgórski

The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…

Probability · Mathematics 2025-02-24 Henrik Bengtsson , Krzysztof Podgorski