Related papers: Time-scale synthesis for locally stationary signal…

This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…

This paper investigates locally linear regression for locally stationary time series and develops theoretical results for locally linear smoothing and transfer learning. Existing analyses have focused on local constant estimators and given…

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…

Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…

A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random…

We introduce the wavelet scattering spectra which provide non-Gaussian models of time-series having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the…

Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…

The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet…

In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…

This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has…

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…

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…