scholarly journals Complete convergence for moving average processes associated to heavy-tailed distributions and applications

2014 ◽  
Vol 420 (1) ◽  
pp. 66-76 ◽  
Author(s):  
Wei Li ◽  
Pingyan Chen ◽  
Tien-Chung Hu
2017 ◽  
Vol 15 (1) ◽  
pp. 467-476
Author(s):  
Li Ge ◽  
Sanyang Liu ◽  
Yu Miao

Abstract In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.


2014 ◽  
Vol 51 (A) ◽  
pp. 267-279 ◽  
Author(s):  
Sidney I. Resnick ◽  
Joyjit Roy

We look at joint regular variation properties of MA(∞) processes of the form X = (Xk, k ∈ Z), where Xk = ∑j=0∞ψjZk-j and the sequence of random variables (Zi, i ∈ Z) are independent and identically distributed with regularly varying tails. We use the setup of MO-convergence and obtain hidden regular variation properties for X under summability conditions on the constant coefficients (ψj: j ≥ 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.


2014 ◽  
Vol 51 (A) ◽  
pp. 267-279
Author(s):  
Sidney I. Resnick ◽  
Joyjit Roy

We look at joint regular variation properties of MA(∞) processes of the form X = (X k , k ∈ Z), where X k = ∑ j=0 ∞ψ j Z k-j and the sequence of random variables (Z i , i ∈ Z) are independent and identically distributed with regularly varying tails. We use the setup of M O -convergence and obtain hidden regular variation properties for X under summability conditions on the constant coefficients (ψ j : j ≥ 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.


2015 ◽  
Vol 25 (1) ◽  
pp. 11-20 ◽  
Author(s):  
M. Amini ◽  
A. Bozorgnia ◽  
H. Naderi ◽  
A. Volodin

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