ASYMPTOTIC THEORY FOR MAXIMUM LIKELIHOOD ESTIMATION OF THE MEMORY PARAMETER IN STATIONARY GAUSSIAN PROCESSES

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1...

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Veröffentlicht in:Econometric theory Jg. 28; H. 2; S. 457 - 470
Hauptverfasser: Lieberman, Offer, Rosemarin, Roy, Rousseau, Judith
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, USA Cambridge University Press 01.04.2012
Cambridge Univ. Press
Cambridge University Press (CUP)
Schlagworte:
Asymptotic theory
Chaos theory
Consistent estimators
Econometrics
Estimating techniques
Estimation
Estimators
Gauss, Carl Friedrich
Mathematical analysis
Mathematics
Maximum likelihood estimation
Maximum likelihood estimators
Maximum likelihood method
Memory
MISCELLANEA
Normality
Parametric models
Spectral energy distribution
Stationarity
Statistics
Statistics Theory
Stochastic processes
Studies
Time series
Time series models
Long Range Dependence
Toeplitz Matrix
Intermediate Memory
Maximum Likelihood Estimation
ISSN:0266-4666, 1469-4360
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Zusammenfassung:Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.
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ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466611000399