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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
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.
Rights and permissions
About this article
Cite this article
D’Elia, A., Piccolo, D. Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation. Statistical Methods & Applications 12, 259–275 (2004). https://doi.org/10.1007/s10260-003-0064-0
Issue Date:
DOI: https://doi.org/10.1007/s10260-003-0064-0