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. © Springer-Verlag 2003.
Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation / D'Elia, A; Piccolo, Domenico. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - STAMPA. - 12:3(2004), pp. 259-275. [10.1007/s10260-003-0064-0]
Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation
PICCOLO, DOMENICO
2004
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. © Springer-Verlag 2003.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.