Invariance principles and central limit theorems for nonadditive, stationary processes

1992 ◽  
pp. 198-228
Author(s):  
Ulrich Wacker
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stationary Processes ◽  
Invariance Principles

Gordin's theorem and the periodogram

1976 ◽  
Vol 13 (02) ◽  
pp. 365-370 ◽  
Author(s):  
Holger Rootzén
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Stationary Sequence ◽  
Central Limit Theorems ◽  
Stationary Processes

In 1968 M. I. Gordin proved a very strong central limit theorem for stationary, ergodic sequences by means of approximation with martingales. In the present paper Gordin's theorem is generalized to cover also the periodogram of a stationary sequence, and the restriction of ergodicity is removed. It is noted that known central limit theorems for stationary processes can often be generalized to the periodogram by means of this result.

Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes

1988 ◽  
Vol 4 (2) ◽  
pp. 210-230 ◽  
Author(s):  
Jeffrey M. Wooldridge ◽  
Halbert White
Keyword(s):  
Stochastic Processes ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Economic Time Series ◽  
Mixing Processes ◽  
Invariance Principles ◽  
Heterogeneous Processes ◽  
Economic Time ◽  
Unit Root Models

Building on work of McLeish, we present a number of invariance principles for doubly indexed arrays of stochastic processes which may exhibit considerable dependence, heterogeneity, and/or trending moments. In particular, we consider possibly time-varying functions of infinite histories of heterogeneous mixing processes and obtain general invariance results, with central limit theorems following as corollaries. These results are formulated so as to apply to economic time series, which may exhibit some or all of the features allowed in our theorems. Results are given for the case of both scalar and vector stochastic processes. Using an approach recently pioneered by Phillips, and Phillips and Durlauf, we apply our results to least squares estimation of unit root models.

Gordin's theorem and the periodogram

1976 ◽  
Vol 13 (2) ◽  
pp. 365-370 ◽  
Author(s):  
Holger Rootzén
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Stationary Sequence ◽  
Central Limit Theorems ◽  
Stationary Processes

In 1968 M. I. Gordin proved a very strong central limit theorem for stationary, ergodic sequences by means of approximation with martingales. In the present paper Gordin's theorem is generalized to cover also the periodogram of a stationary sequence, and the restriction of ergodicity is removed. It is noted that known central limit theorems for stationary processes can often be generalized to the periodogram by means of this result.

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