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- W1963899503 abstract "Abstract Extending the results in Sargan (Citation1976) and Tanaka (Citation1984), we derive the asymptotic expansions of the distribution, the bias and the mean squared error of the MM and QML estimators of the first-order autocorrelation and the MA parameter for the MA(1) model. It turns out that the asymptotic properties of the estimators depend on whether the mean of the process is known or estimated. A comparison of the moment expansions, either in terms of bias or MSE, reveals that there is not uniform superiority of neither of the estimators, when the mean of the process is estimated. This is also confirmed by simulations. In the zero-mean case, and on theoretical grounds, the QMLEs are superior to the MM ones in both bias and MSE terms. We also discuss how the approximations are affected by moderate deviations from the unit root case. The results presented here are important for bias correction and increasing the efficiency of the estimators. Keywords: Asymptotic propertiesBias correctionFirst order autocorrelationMethod of momentsMoving average processNear unit rootQuasi maximum likelihoodMathematics Subject Classification: C10C22 Acknowledgment The article has not been published elsewhere and it has not been submitted simultaneously for publication elsewhere. We are grateful to Stelios Arvanitis, the participants at the 18th EC2 Conference in Faro, Portugal and the seminar participants at the University of Piraeus. Financial support from the Basic Research Funding Program (PEVE 2) is gratefully acknowledged. Full responsibility for all shortcomings is our. Notes Nagar (Citation1959), Sargan (Citation1974), Phillips (Citation1977), Tanaka (Citation1984), Kakizawa (Citation1999), and Ogasawara (Citation2006) to quote only a few articles. Rothenberg (Citation1986) gave a review on the asymptotic techniques employed in econometrics. For a book treatment of Edgeworth expansions, see, e.g., Hall (Citation1992), Barndorff-Nielsen and Cox (Citation1989), and Taniguchi and Kakizawa (Citation2000). From now on, we will refer to the up to order expansion as first-order one and for the up to n −1 order as second-order expansion, where n is the sample size. For an alternative methodology based on a Whittle-type estimator, see Taniguchi (Citation1987), Lieberman et al. (Citation2003), and Andrews and Lieberman (Citation2005). Aga (Citation2011) extending the results of Lieberman et al. (Citation2003), provided an Edgeworth expansion for linear regression process with stationary Gaussian long memory errors. All the cumulants needed for the estimators, as well as the Edgeworth coefficients of all the expansions are presented in an extensive Technical Appendix that the authors have created if the readers are interested in the detailed proofs. For various approximations of the MLE see Davidson (Citation1981). Notes. “Bias Feas.” stands for the feasibly bias corrected estimator, i.e., when the estimated value of the parameter is employed for bias correction (the same applies to all tables)." @default.
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- W1963899503 date "2013-05-15" @default.
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- W1963899503 title "Edgeworth and Moment Approximations: The Case of MM and QML Estimators for the MA(1) Models" @default.
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- W1963899503 doi "https://doi.org/10.1080/03610926.2011.597919" @default.
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