Related papers: A simple test for white noise in functional time s…
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
In this paper, we give the white noise calculus for the Fermion system and prove the Fock expansion. Each continuous linear operator on Fermionic white noise functionals is uniquely represented by the series of integral kernel operators.…
We review existing methods for generating long streams of 1/f^alpha noise ($0<\alpha\le 2$) focusing on the digital filtering of white noise. We detail the formalism to conceive an efficient random number generator (white outside some…
We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process, which contains the covariance operator of the corresponding FLR model in its…
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…
Noise simulation is a very powerful tool in signal analysis helping to foresee the system performance in real experimental situations. Time series generation is however a hard challenge when a robust model of the noise sources is missing.…
We propose a new testing procedure for detecting localized departures from monotonicity of a signal embedded in white noise. In fact, we perform simultaneously several tests that aim at detecting departures from concavity for the integrated…
This paper proposes a new multi-linear projection method for denoising and estimation of high-dimensional matrix-variate factor time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent,…
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…
Estimating the spectral density function $f(w)$ for some $w\in [-\pi, \pi]$ has been traditionally performed by kernel smoothing the periodogram and related techniques. Kernel smoothing is tantamount to local averaging, i.e., approximating…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This paper aims…
Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…
Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes,…
An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a…
Power spectral densities are a common, convenient, and powerful way to analyze signals. So much so that they are now broadly deployed across the sciences and engineering---from quantum physics to cosmology, and from crystallography to…
This paper proposes a new family of multi-frequency-band (MFB) tests for the white noise hypothesis by using the maximum overlap discrete wavelet packet transform (MODWPT). The MODWPT allows the variance of a process to be decomposed into…
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time…
We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…