Related papers: The V/S test of long-range dependence in random fi…
In recent years, long short-term memory (LSTM) has been successfully used to model sequential data of variable length. However, LSTM can still experience difficulty in capturing long-term dependencies. In this work, we tried to alleviate…
This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter, typically an I(d) series with d>-.5. The…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
This paper introduces a novel methodology that utilizes latency to unveil time-series dependence patterns. A customized statistical test detects memory dependence in event sequences by analyzing their inter-event time distributions.…
The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to now. A great deal of such theory focused on \textit{iid} or…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue…
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…
We consider an estimator for the location of a shift in the mean of long-range dependent sequences. The estimation is based on the two-sample Wilcoxon statistic. Consistency and the rate of convergence for the estimated change point are…
In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
In this paper, we consider isotropic and stationary real Gaussian random fields defined on $\mathbb{S}^2\times\mathbb{R}$ and we investigate the asymptotic behavior, as $T\rightarrow +\infty$, of the empirical measure (excursion area) in…