On the sample mean of locally stationary long-memory processes

@article{Palma2010OnTS,
  title={On the sample mean of locally stationary long-memory processes},
  author={Wilfredo Palma},
  journal={Journal of Statistical Planning and Inference},
  year={2010},
  volume={140},
  pages={3764-3774}
}
  • W. Palma
  • Published 1 December 2010
  • Mathematics
  • Journal of Statistical Planning and Inference
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16 Citations
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16 Citations

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References

SHOWING 1-10 OF 22 REFERENCES
On parameter estimation for locally stationary long-memory processes
ON THE EFFICIENCY OF THE SAMPLE MEAN IN LONG‐MEMORY NOISE
. When estimating the unknown mean of a stationary time series, the best linear unbiased estimator is often a significantly better estimator than the ordinary least squares estimates Xn. The relative…
Statistics for long-memory processes
TLDR
Theorems of Stationary Processes with Long Memory Limit Theorems and Estimations of Long Memory-Heuristic Approaches, Forecasting Regression Goodness of Fit Tests, and Robust Estimation of Long memory estimates are presented.
Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series
Behavior of sample means and nonparametric time-series estimation
TLDR
This paper consists of five sections discussing notation; spectral density classification of memory type of a time series; equivalent degrees of freedom of asymptotic confidence intervals for the mean; sample Fourier transforms and sample spectral density; sample Brownian Bridge functionals and standardized time series.
THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS
Abstract. The definitions of fractional Gaussian noise and integrated (or fractionally differenced) series are generalized, and it is shown that the two concepts are equivalent. A new estimator of…
Long-Memory Time Series: Theory and Methods
Preface. Acronyms. 1. Stationary Processes. 2. State Space Systems. 3. Long-Memory Processes. 4. Estimation Methods. 5. Asymptotic Theory. 6. Heteroskedastic Models. 7. Transformations. 8. Bayesian…
Locally stationary random processes
TLDR
In the case of locally stationary random processes, a relation is found between the covariance and the spectral density which constitutes a natural generalization of the Wiener-Khintchine relations.
On a time deformation reducing nonstationary stochastic processes to local stationarity
A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize…
Quantile spectral analysis and long-memory time series
  • E. Parzen
  • Computer Science
    Journal of Applied Probability
  • 1986
An approach to time series model identification is described which involves the simultaneous use of frequency, time and quantile domain algorithms; the approach is called quantile spectral analysis.…
...
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