Related papers: Spectral Simulation of Functional Time Series
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…
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…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
We propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the $L^2$-distance between the spectral density operator of a non-stationary process and its best ($L^2$-)approximation…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density estimators…
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap…
We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the $L^2$-distance between the spectral density operator and its best ($L^2$-)approximation by a spectral…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…
This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series (LSFTS). We investigate a kernel-based method to estimate the time-varying covariance operator and the…
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…
The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…
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…
In this paper, we investigate the stationarity of stochastic processes in the fractional Fourier domains. We study the stationarity of a stochastic process after performing fractional Fourier transform (FRFT), and discrete fractional…
Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…
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…