Related papers: A highly specific test for periodicity
In this paper, we analyze several instrumental records of temperatures at different locations by using new techniques originally developed for the analysis of extreme values of dynamical systems. We show that they have the same recurrence…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
Given a pair of multivariate time-series data of the same length and dimensions, an approach is proposed to select variables and time intervals where the two series are significantly different. In applications where one time series is an…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
The continued digitization of societal processes translates into a proliferation of time series data that cover applications such as fraud detection, intrusion detection, and energy management, where anomaly detection is often essential to…
The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary…
Astrophysical objects frequently exhibit some irregularities or complex behaviour in their light curves. We focus primarily on hot stars, where both radial and non-radial pulsations are observed. One of the primary research goals is to…
The issue of inheriting periodicity of an exact solution of a dynamic system by a difference scheme is considered. It is shown that some difference schemes (midpoint scheme, Kahan scheme) in some special cases provide approximate solutions…
The field of time series anomaly detection is constantly advancing, with several methods available, making it a challenge to determine the most appropriate method for a specific domain. The evaluation of these methods is facilitated by the…
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerful method uses differential equations to approximate the…
Oftentimes in practice, the observed process changes statistical properties at an unknown point in time and the duration of a change is substantially finite, in which case one says that the change is intermittent or transient. We provide an…
Time-series stationarity is a property that statistical characteristics such as trend, variance, seasonality remain constant over time. It is considered fundamental to many forecasting and analysis methods. Different tests detect different…
Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume…
We propose a new sequential procedure to detect change in the parameters of a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models (such as AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH processes). The…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since…
In this paper, we first give the definition of random almost periodic solutions of random dynamical systems and give some examples. Then, we prove the existence of such random almost periodic solutions. Further, we introduce the definition…