Summation of weakly dependent sequences by Cesàro methods

V. F. Gaposhkin

doi:10.1007/bf01909433

The Bahadur representation of sample quantiles for weakly dependent sequences

Stochastics ◽

10.1080/17442508.2015.1085537 ◽

2015 ◽

Vol 88 (3) ◽

pp. 428-436 ◽

Cited By ~ 4

Author(s):

Yiwei Wang ◽

Wenzhi Yang ◽

Shuhe Hu

Keyword(s):

Bahadur Representation ◽

Weakly Dependent Sequences ◽

Sample Quantiles ◽

Weakly Dependent

The Central Limit Theorem for Some Weakly Dependent Sequences

Theory of Probability and Its Applications ◽

10.1137/1115073 ◽

1970 ◽

Vol 15 (4) ◽

pp. 649-666 ◽

Cited By ~ 3

Author(s):

V. F. Gaposhkin

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

The Central Limit Theorem ◽

Weakly Dependent Sequences ◽

Weakly Dependent

Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences

ESAIM Probability and Statistics ◽

10.1051/ps:2005003 ◽

2005 ◽

Vol 9 ◽

pp. 38-73 ◽

Cited By ~ 3

Author(s):

Jérôme Dedecker ◽

Sana Louhichi

Keyword(s):

Finite Variance ◽

Infinitely Divisible Distributions ◽

Infinitely Divisible ◽

Weakly Dependent Sequences ◽

Weakly Dependent

A Note on Exponential Inequalities of ψ-Weakly Dependent Sequences

Communications for Statistical Applications and Methods ◽

10.5351/csam.2014.21.3.245 ◽

2014 ◽

Vol 21 (3) ◽

pp. 245-251 ◽

Cited By ~ 2

Author(s):

Eunju Hwang ◽

Dong Wan Shin

Keyword(s):

Exponential Inequalities ◽

Weakly Dependent Sequences ◽

Weakly Dependent

On the central limit theorem for weakly dependent sequences with a decomposed strong mixing coefficient

Stochastic Processes and their Applications ◽

10.1016/0304-4149(92)90034-n ◽

1992 ◽

Vol 42 (2) ◽

pp. 181-193 ◽

Cited By ~ 8

Author(s):

Magda Peligrad

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Strong Mixing ◽

Mixing Coefficient ◽

The Central Limit Theorem ◽

Weakly Dependent Sequences ◽

Weakly Dependent

The central limit theorem for summability methods of some weakly dependent sequences

Statistics & Probability Letters ◽

10.1016/0167-7152(87)90070-8 ◽

1987 ◽

Vol 5 (2) ◽

pp. 143-147

Author(s):

Ken-ichi Yoshihara ◽

Hiroshi Takahata

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

The Central Limit Theorem ◽

Summability Methods ◽

Weakly Dependent Sequences ◽

Weakly Dependent

A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables

The Annals of Probability ◽

10.1214/aop/1176993379 ◽

1984 ◽

Vol 12 (1) ◽

pp. 141-153 ◽

Cited By ~ 151

Author(s):

Norbert Herrndorf

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Random Variables ◽

Functional Central Limit Theorem ◽

Weakly Dependent Sequences ◽

Functional Central Limit ◽

Weakly Dependent

IMPULSE RESPONSES OF FRACTIONALLY INTEGRATED PROCESSES WITH LONG MEMORY

Econometric Theory ◽

10.1017/s0266466610000216 ◽

2010 ◽

Vol 26 (6) ◽

pp. 1855-1861 ◽

Cited By ~ 18

Author(s):

Uwe Hassler ◽

Piotr Kokoszka

Keyword(s):

Long Memory ◽

Necessary And Sufficient Condition ◽

Impulse Responses ◽

Short Memory ◽

Weakly Dependent Sequences ◽

Integrated Time Series ◽

Necessary And Sufficient ◽

Fractional Filter ◽

Weakly Dependent ◽

Integrated Processes

Fractionally integrated time series, which have become an important modeling tool over the last two decades, are obtained by applying the fractional filter $(1 - L)^{ - d} = \sum\nolimits_{n = 0}^\infty {b_n } L^n$ to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response coefficients of their Wold representation. The weights bn decay at the rate nd−1 and are not absolutely summable for long memory models (d > 0). It has been believed that this rate is inherited by the impulse responses of any long memory fractionally integrated model. We show that this conjecture does not hold in such generality, and we establish a simple necessary and sufficient condition for the rate nd−1 to be inherited by fractionally integrated processes.

Transportation inequalities for weakly dependent sequences

Acta Mathematica Scientia ◽

10.1016/s0252-9602(11)60335-4 ◽

2011 ◽

Vol 31 (4) ◽

pp. 1494-1502

Author(s):

Ma Yutao

Keyword(s):

Weakly Dependent Sequences ◽

Weakly Dependent

Consistency of a hybrid block bootstrap for distribution and variance estimation for sample quantiles of weakly dependent sequences

Australian & New Zealand Journal of Statistics ◽

10.1111/anzs.12206 ◽

2018 ◽

Vol 60 (1) ◽

pp. 103-114 ◽

Cited By ~ 1

Author(s):

Todd A. Kuffner ◽

Stephen M. S. Lee ◽

G. A. Young

Keyword(s):

Variance Estimation ◽

Block Bootstrap ◽

Weakly Dependent Sequences ◽

Sample Quantiles ◽

Weakly Dependent