Moment convergence rates in the law of logarithm for moving average process under dependence

Stochastics ◽  
2013 ◽  
Vol 86 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Xiaoyong Xiao ◽  
Hongwei Yin
Keyword(s):  
Convergence Rates ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Moment Convergence ◽  
The Law

scholarly journals Complete Convergence for Moving Average Process of Martingale Differences

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wenzhi Yang ◽  
Shuhe Hu ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Martingale Differences ◽  
Moment Convergence ◽  
Moving Process

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones.

Convergence rates in the complete moment of moving-average processes

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
Qing-pei Zang
Keyword(s):  
Convergence Rates ◽  
Infinite Sequence ◽  
Moving Average ◽  
Precise Asymptotics ◽  
Moving Average Process ◽  
Real Numbers ◽  
Moment Convergence ◽  
Summable Sequence ◽  
Moving Average Processes ◽  
Independent Identically Distributed

AbstractIn this paper, we discuss precise asymptotics for a new kind of moment convergence of the moving-average process $$X_k = \sum\limits_{i = - \infty }^\infty {a_{i + k} \varepsilon _i }$$, k ≥1, where {ε i: −∞ < i < ∞} is a doubly infinite sequence of independent identically distributed random variables with mean zero and the finiteness of variance, {α i: −∞ < i < ∞} is an absolutely summable sequence of real numbers, i.e., $$\sum\limits_{i = - \infty }^\infty {\left| {a_i } \right| < \infty }$$.

Sign in / Sign up

Export Citation Format

Share Document