English
Related papers

Related papers: Ordinal Patterns in Long-Range Dependent Time Seri…

200 papers

The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability…

Probability · Mathematics 2008-06-19 G. Morvai , S. Yakowitz , L. Gyorfi

The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…

Statistics Theory · Mathematics 2019-07-23 Holger Drees , Miran Knezevic

Consider two batches of independent or interdependent exponentiated location-scale distributed heterogeneous random variables. This article investigates ordering results for the second-order statistics from these batches when a vector of…

Statistics Theory · Mathematics 2021-04-20 Sangita Das , Suchandan Kayal

For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d=2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns…

Probability · Mathematics 2008-01-11 Mathieu Sinn , Karsten Keller

The increasing occurrence of ordinal data, mainly sociodemographic, led to a renewed research interest in ordinal regression, i.e. the prediction of ordered classes. Besides model accuracy, the interpretation of these models itself is of…

Machine Learning · Computer Science 2019-02-21 Lukas Pfannschmidt , Jonathan Jakob , Michael Biehl , Peter Tino , Barbara Hammer

A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…

Neurons and Cognition · Quantitative Biology 2018-06-29 Yanlong Sun , Hongbin Wang

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…

Statistics Theory · Mathematics 2026-01-21 Annika Betken , Giorgio Micali , Manuel Ruiz Marín

A permutation $\sigma$ describing the relative orders of the first $n$ iterates of a point $x$ under a self-map $f$ of the interval $I=[0,1]$ is called an \emph{order pattern}. For fixed $f$ and $n$, measuring the points $x\in I$ (according…

Combinatorics · Mathematics 2010-03-30 Aaron Abrams , Eric Babson , Henry Landau , Zeph Landau , James Pommersheim

These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity…

Econometrics · Economics 2023-08-15 Christis Katsouris

The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are…

Statistics Theory · Mathematics 2021-04-20 Sangita Das , Suchandan Kayal

The stochastic comparisons of parallel and series system are worthy of study. In this paper, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution with two parameters…

Statistics Theory · Mathematics 2019-05-03 Surojit Biswas , Nitin Gupta

We consider random hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that…

Probability · Mathematics 2007-10-21 Greg Anderson , Ofer Zeitouni

Hermite processes are self--similar processes with stationary increments which appear as limits of normalized sums of random variables with long range dependence. The Hermite process of order $1$ is fractional Brownian motion and the…

Probability · Mathematics 2014-07-22 Marianne Clausel , François Roueff , Murad Taqqu , Ciprian A. Tudor

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

Probability · Mathematics 2020-02-13 Marie-Christine Düker

The Hermite rank appears in limit theorems involving long memory. We show that an Hermite rank higher than one is unstable when the data is slightly perturbed by transformations such as shift and scaling. We carry out a "near higher order…

Statistics Theory · Mathematics 2018-01-09 Shuyang Bai , Murad s. Taqqu

Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp.…

Applications · Statistics 2016-01-18 Amarjit Kundu , Shovan Chowdhury , Asok K. Nanda , Nil Kamal Hazra

In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic…

Probability · Mathematics 2008-05-13 Mathew D. Penrose , Andrew R. Wade

In this manuscript, we study stochastic comparisons of the second-order statistics from dependent or independent observations with modified proportional hazard rates models. First, we establish the usual stochastic order of the second-order…

Statistics Theory · Mathematics 2022-01-06 Niu Jiale

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…

Statistics Theory · Mathematics 2010-11-12 Wilfredo Palma , Ricardo Olea

Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this…

Statistics Theory · Mathematics 2021-10-13 M. Dolores Ruiz-Medina