Functional CLT for nonstationary strongly mixing processes

2020 ◽  
Vol 156 ◽  
pp. 108581 ◽  
Author(s):  
Florence Merlevède ◽  
Magda Peligrad
Keyword(s):  
Mixing Processes ◽  
Functional Clt ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (4) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (04) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

Finite state bilaterally deterministic strongly mixing processes

1996 ◽  
Vol 95 (1) ◽  
pp. 115-133 ◽  
Author(s):  
Robert M. Burton ◽  
Manfred Denker ◽  
Meir Smorodinsky
Keyword(s):  
Mixing Processes ◽  
Strongly Mixing ◽  
Finite State ◽  
Strongly Mixing Processes

scholarly journals BLOCK BOOTSTRAP CONSISTENCY UNDER WEAK ASSUMPTIONS

2018 ◽  
Vol 34 (6) ◽  
pp. 1383-1406 ◽  
Author(s):  
Gray Calhoun
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Partial Sums ◽  
Block Bootstrap ◽  
Mixing Processes ◽  
Bootstrap Methods ◽  
Moment Conditions ◽  
Sample Mean ◽  
Functional Clt

This paper weakens the size and moment conditions needed for typical block bootstrap methods (i.e., the moving blocks, circular blocks, and stationary bootstraps) to be valid for the sample mean of Near-Epoch-Dependent (NED) functions of mixing processes; they are consistent under the weakest conditions that ensure the original NED process obeys a central limit theorem (CLT), established by De Jong (1997, Econometric Theory 13(3), 353–367). In doing so, this paper extends De Jong’s method of proof, a blocking argument, to hold with random and unequal block lengths. This paper also proves that bootstrapped partial sums satisfy a functional CLT (FCLT) under the same conditions.

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