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Prediction in the frequency domain under long-range processes with application to the signal extraction problem

Hidalgo, Javier and Yajima, Y. (2002) Prediction in the frequency domain under long-range processes with application to the signal extraction problem. Econometric Theory, 18 (03). pp. 584-624. ISSN 0266-4666

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Identification Number: 10.1017/S0266466602183022


We frequently observe that one of the aims of time series analysts is to predict future values of the data. For weakly dependent data, when the model is known up to a finite set of parameters, its statistical properties are well documented and exhaustively examined. However, if the model was misspecified, the predictors would no longer be correct. Motivated by this observation and because of the interest in obtaining adequate and reliable predictors, Bhansali (1974, Journal of the Royal Statistical Society, Series B 36, 61-73) examined the properties of a nonparametric predictor based on the canonical factorization of the spectral density function given in Whittle (1963, Prediction and Regulation by Linear Least Squares) and known as FLES. However, the preceding work does not cover the so-called strongly dependent data. Because of the interest in this type of processes, one of our objectives in this paper is to examine the properties of the FLES for these processes. In addition, we illustrate how the FLES can be adapted to recover the signal of a strongly dependent process, showing its consistency. The proposed method is semiparametric in the sense that, in contrast to other methods, we do not need to assume any particular model for the noise except that it is weakly dependent.

Item Type: Article
Official URL:
Additional Information: © 2002 Cambridge University Press
Divisions: Economics
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Sets: Departments > Economics
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Date Deposited: 18 Apr 2011 15:09
Last Modified: 20 Feb 2021 03:37

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