Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation |
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Authors: | Email author" target="_blank">Angela?D’EliaEmail author Domenico?Piccolo |
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Institution: | (1) Dipartimento di Scienze Statistiche, Universitá degli Studi di Napoli Federico II, Via L. Rodinó 22, 80138 Napoli, Italy |
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Abstract: | In this paper we study the interaction between the estimation of the fractional differencing parameter d of ARFIMA models and the common practice of instantaneous transformation of the observed time series. At this aim, we first discuss the effect of a nonlinear transformation of the data on the identification of the process and on the estimate of d. Thus, we propose a joint estimation of the Box-Cox parameter and d by means of a modified normalized version of the Whittle likelihood. Then, the variance and covariance matrix of the parameters estimates is obtained. Finally, a Monte Carlo study is performed in order to check the behaviour of the proposed estimators in finite samples.The paper is the result of a joint research of the two authors. As far as it concerns this version of the work, A. D Elia wrote Sects. 2, 3, 4, while D. Piccolo wrote Sects. 1, 5, 6. |
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Keywords: | ARFIMA models Box-Cox transformation Normalized Whittle likelihood |
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