CENTRAL LIMIT THEOREMS FOR FINITE WALSH-FOURIER TRANSFORMS OF WEAKLY STATIONARY TIME SERIES

1985 ◽  
Vol 6 (4) ◽  
pp. 261-267 ◽  
Author(s):  
David S. Stoffer
Keyword(s):  
Time Series ◽  
Central Limit ◽  
Limit Theorems ◽  
Fourier Transforms ◽  
Central Limit Theorems ◽  
Stationary Time Series ◽  
Stationary Time

scholarly journals Central limit theorems for sequential and random intermittent dynamical systems

2016 ◽  
Vol 38 (3) ◽  
pp. 1127-1153 ◽  
Author(s):  
MATTHEW NICOL ◽  
ANDREW TÖRÖK ◽  
SANDRO VAIENTI
Keyword(s):  
Time Series ◽  
Fixed Point ◽  
Dynamical Systems ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stationary Time Series ◽  
Stationary Time

We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the Pomeau–Manneville map. We also obtain quenched central limit theorems for random compositions of these maps.

Estimation of the mean of a stationary time series by sampling

1973 ◽  
Vol 10 (02) ◽  
pp. 419-431 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Stationary Point ◽  
Limit Theorems ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Stationary Point Process ◽  
The Mean ◽  
The Times ◽  
Sampling Times

LetX(t), – ∞ <t< ∞, be a stationary time series with meancx. Let 0 <τ1<τ2 < … <τN≦Tdenote A given sampling times in the interval (0,T]. We determine the asymptotic distribution of the estimate [X(τ1) + … +X(τN)]/Nofcxwhen the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the seriesX(t). The results obtained may be viewed as non-standard central limit theorems.

Estimation of the mean of a stationary time series by sampling

1973 ◽  
Vol 10 (2) ◽  
pp. 419-431 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Stationary Point ◽  
Limit Theorems ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Stationary Point Process ◽  
The Mean ◽  
The Times ◽  
Sampling Times

Let X(t), – ∞ < t < ∞, be a stationary time series with mean cx. Let 0 < τ1 < τ2 < … < τN ≦ T denote A given sampling times in the interval (0, T]. We determine the asymptotic distribution of the estimate [X(τ1) + … + X(τN)]/N of cx when the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the series X(t). The results obtained may be viewed as non-standard central limit theorems.

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