Related papers: A simple test for white noise in functional time s…
We propose a general white noise test for functional time series based on estimating a distance between the spectral density operator of a weakly stationary time series and the constant spectral density operator of an uncorrelated time…
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…
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…
We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the…
Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this…
We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general…
In this paper we develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time…
We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non-stationary time…
The problem of testing equality of the entire second order structure of two independent functional linear processes is considered. A fully functional $L^2$-type test is developed which evaluates, over all frequencies, the Hilbert-Schmidt…
We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses any such stationary functional time series, whether linear…
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
This article proposes a novel test for the martingale difference hypothesis based on the martingale difference divergence function, a recently developed dependence measure suitable for measuring the degree of conditional mean dependence of…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
A spatial-sign based test procedure is proposed for high dimensional white noise test in this paper. We establish the limit null distribution and give the asymptotical relative efficient of our test with respect to the test proposed by Feng…
A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional…
We consider the statistical experiment given by a sample of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam's deficiency Delta-distance, to two Gaussian experiments…
This paper is concerned with inference based on the mean function of a functional time series, which is defined as a collection of curves obtained by splitting a continuous time record, e.g. into daily or annual curves. We develop a normal…
Testing for multi-dimensional white noise is an important subject in statistical inference. Such test in the high-dimensional case becomes an open problem waiting to be solved, especially when the dimension of a time series is comparable to…
We propose a new omnibus test for vector white noise using the maximum absolute auto-correlations and cross-correlations of the component series. Based on the newly established approximation by the $L_\infty$-norm of a normal random vector,…
In this paper, we present a general framework for testing relevant hypotheses in functional time series. Our unified approach covers one-sample, two-sample, and change point problems under contaminated observations with arbitrary sampling…