PREDICTION AND SIGNAL EXTRACTION OF STRONGLY DEPENDENT PROCESSES IN THE FREQUENCY DOMAIN* by J Hidalgo London School of Economics and Political Science and Y. Yajima University of Tokyo
Contents: Abstract 1. Introduction 2. The FLES Algorithm and its Estimator 3. Asymptotic Properties of the Estimators 4. Signal Extraction 5. Extension to Seasonal / Cyclical Data 6. Proofs 7. Technical Lemmas 8. Conclusions and Extensions References
Discussion Paper No.EM/01/418 June 2001
*
The Suntory Centre Suntory and Toyota International Centres for Economics and Related Disciplines London School of Economics and Political Science Houghton Street London WC2A 2AE Tel.: 020-7955 6698
The first author gratefully acknowledges the research support of the Economic and Social Research Council (ESRC), reference number: R000238212. The second author gratefully acknowledges the research support of the Ministry of Education of Japan, reference number: 09CE20012.
Abstract 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 due to the interest in obtaining adequate and reliable predictors, Bhansali (1974) examined the properties of a nonparametric predictor based on the canonical factorization of the spectral density function given in Whittle (1963) and known as FLES. However, the above work does not cover the so-called strongly dependent data. Due to the interest in this type of process, 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. Keywords: Prediction; strong dependence; spectral density function; canonical factorization; signal extraction. JEL Nos.: C22, C53.
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Contact address: Dr Javier Hidalgo, Department of Economics, London School of Economics and Political Science, Houghton Street, London WC2 2AE, UK. Email:
[email protected]
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