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WHITTLE PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION
FOR NONSTATIONARY TIME SERIES
*
by
Carlos Velasco
Universidad Carlos III, Madrid
and
Peter M Robinson
London School of Economics and Political Science
Contents:
Abstract
1.  Introduction
2.  The Model and the Discrete
Fourier Transform
3.  Whittle Estimates
4.  Simulation Results
5.  Illustrative Examples
6.  Appendix A: Technical Assumptions
and Results
7.  Appendix B: Proofs
References
The Suntory Centre
Suntory and Toyota International Centres
for Economics and Related Disciplines
London School of Economics and Political
Science
Discussion Paper
Houghton Street
No. EM/00/391
London WC2A 2AE
May 2000
Tel.: 020-7405 7686
The research of the first author was supported by Spanish Direccion General de
Ensenanza  Superior, Ref.  No.  PB98-0025. The  second  author’s research  was
supported by ESRC Grant No. R000235892, and a Leverhulme Trust Personal
Professorship. The authors thank the editor, the associate editor and the referees for
very helpful comments.
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Abstract
Whittle pseudo-maximum likelihood estimates of parameters for stationary
time series have been found to be consistent and asumptotically normal in the
presence  of  long-range  dependence.  Generalizing  the  definition  of  the
memory  parameter d,  we  extend  these  results  to  include  possibly
nonstationary (0.5 
d < 1) or antipersistent (-0.5 < d < 0) observations. Using
adequate data tapers we can apply this estimation technique to any degree of
nonstationarity d 

We analyse the performance of the estimates on simulated and real data.
Keywords: Long-range dependence; nonstationary long memory time series;
nonstationary fractional models; frequency domain estimation; tapering.
JEL No.: C22
© 
by the authors. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full
credit, including © notice, is given to the source.
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