Open Access
November, 1977 Estimation in the First Order Moving Average Model Based on Sample Autocorrelations
Raul Pedro Mentz
Ann. Statist. 5(6): 1250-1257 (November, 1977). DOI: 10.1214/aos/1176344012


For the first order moving average we consider a proposal by Walker (Biometrika, 1961) to use $k$ sample autocorrelations $(1 < k < T, T$ sample size), to estimate the first autocorrelation of the model, and hence its basic parameter. When $k = k_T \rightarrow \infty$ as $T \rightarrow \infty$, the estimator is proved consistent and asymptotically normal and efficient, the latter provided $k_T$ dominates $\log T$ and is dominated by $T^\frac{1}{2}$. An alternative form of the estimator facilitates the calculations and the analysis of the role of $k$, without changing the asymptotic properties.


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Raul Pedro Mentz. "Estimation in the First Order Moving Average Model Based on Sample Autocorrelations." Ann. Statist. 5 (6) 1250 - 1257, November, 1977.


Published: November, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0376.62061
MathSciNet: MR448765
Digital Object Identifier: 10.1214/aos/1176344012

Primary: 62M10
Secondary: 62M99

Keywords: approximate maximum likelihood estimation , consistent and asymptotically efficient estimators , First order moving average model

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • November, 1977
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