Related papers: The Permutation-Spectrum Test: Identifying Periodi…
Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the…
We show that while the Fourier transform can figure only an "intensity" of a periodic signal, there is an additional information embedded, which is a "coherence" of the signal. Supposing that the periodicity is reflected only on the…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
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…
Motivated by the need to statistically quantify differences between modern (complex) data-sets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
The usual procedure for estimating the significance of a peak in a power spectrum is to calculate the probability of obtaining that value or a larger value by chance (known as the "p-value"), on the assumption that the time series contains…
We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…
Fluctuation-enhanced sensing comprises the analysis of the stochastic component of the sensor signal and the utilization of the microscopic dynamics of the interaction between the agent and the sensor. We study the relationship between the…
Contagion arising from clustering of multiple time series like those in the stock market indicators can further complicate the nature of volatility, rendering a parametric test (relying on asymptotic distribution) to suffer from issues on…
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…
We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an…
Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…
We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A noise-uncertainty-free detector that is optimal in the low signal to noise ratio regime is analyzed in such a…