Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation

Angela D’Elia () and Domenico Piccolo ()
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Angela D’Elia: Universitá degli Studi di Napoli Federico II
Domenico Piccolo: Universitá degli Studi di Napoli Federico II

Statistical Methods & Applications, 2004, vol. 12, issue 3, No 1, 259-275

Abstract: 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.

Keywords: ARFIMA models; Box-Cox transformation; Normalized Whittle likelihood (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s10260-003-0064-0

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