This article reviews the role of wavelets in statistical time–series analysis. We survey work
that emphasizes scale, such as estimation of variance, and the scale exponent of processes …

The word 'multiscale'can mean many things. However, in this book we are generally
concerned with the representation of objects at a set of scales and then manipulating these …

This paper defines and studies a new class of non‐stationary random processes constructed
from discrete non‐decimated wavelets which generalizes the Cramér (Fourier) …

The article contains an overview over locally stationary processes. At the beginning, time
varying autoregressive processes are discussed in detail–both as a deep example and an …

Wavelets are mathematical expansions that transform data from the time domain into
different layers of frequency levels. Compared to standard Fourier analysis, they have the …

Many time series are not second order stationary and it is not appropriate to analyse them by
using methods designed for stationary series. The paper introduces a new test for second …

We consider a zero mean discrete time series, and define its discrete Fourier transform
(DFT) at the canonical frequencies. It can be shown that the DFT is asymptotically …

Testing for stationarity of functional time series in the frequency domain Page 1 The Annals of
Statistics 2020, Vol. 48, No. 5, 2505–2547 https://doi.org/10.1214/19-AOS1895 © Institute of …

We anticipate noise from the Laser Interferometer Space Antenna (LISA) will exhibit
nonstationarities throughout the duration of its mission due to factors such as antenna …

In this article we investigate the problem of measuring deviations from stationarity in locally
stationary time series. Our approach is based on a direct estimate of the L 2-distance …