Related papers: Modeling Nonstationary Time Series using Locally S…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

In this paper we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type statistic, which…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…

A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing…

Time series foundation models (TSFMs) are widely used as generic feature extractors, yet the notion of non-stationarity in their embedding spaces remains poorly understood. Recent work often conflates non-stationarity with distribution…

In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is ``stationarity'', which reflects the underlying dynamic behavior and is crucial across various…

We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary, or locally stationary, time…

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…

A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…

Parametric modeling of non-stationary signals is addressed in this article. We present several models based on the characteristic features of the modeled signal, together with the methods for accurate estimation of model parameters.…

This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…

We present online prediction methods for time series that let us explicitly handle nonstationary artifacts (e.g. trend and seasonality) present in most real time series. Specifically, we show that applying appropriate transformations to…

We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are…

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are…

This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…