The Asymptotic Behavior of the Prediction Error of a Stationary Sequence with a Spectral Density of Special Type

1968 ◽  
Vol 13 (4) ◽  
pp. 703-707 ◽  
Author(s):  
I. A. Ibragimov ◽  
V. N. Solev
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Prediction Error ◽  
Stationary Sequence

On exponential decay of the variance of BLUE for the mean of a stationary sequence

2019 ◽  
Vol 56 (4) ◽  
pp. 482-491
Author(s):  
Nikolay Babayan ◽  
Mamikon S. Ginovyan
Keyword(s):  
Spectral Density ◽  
Unbiased Estimator ◽  
Sufficient Conditions ◽  
Stationary Sequence ◽  
Necessary Condition ◽  
Positive Lebesgue Measure ◽  
Best Linear Unbiased Estimator ◽  
Exponential Rate ◽  
Best Linear Unbiased ◽  
The Mean

Abstract In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

Asymptotic Behavior of Temporal Aggregates in the Frequency Domain

2013 ◽  
Vol 5 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Uwe Hassler ◽  
Henghsiu Tsai
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Spectral Density ◽  
Frequency Domain ◽  
Fractional Integration ◽  
Integrated Processes

AbstractThe classical aggregation result by Tiao (1972, Asymptotic Behavior of Temporal Aggregates of Time Series, Biometrika 59, 525–531) is generalized for a weak set of assumptions. The innovations driving the integrated processes are only required to be stationary with integrable spectral density. The derivation is settled in the frequency domain. In case of fractional integration, it is demonstrated that the order of integration is preserved with growing aggregation under the same set of assumptions.

On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (03) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say by minimizing two criteria D 1 (·), D 2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

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