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TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

Published online by Cambridge University Press:  01 July 2019

Javier Hualde  and
Morten Ørregaard Nielsen
Javier Hualde
Affiliation:
Universidad Pública de Navarra
Morten Ørregaard Nielsen*
Affiliation:
Queen’s University and CREATES
*
Address correspondence to Morten Ørregaard Nielsen, Department of Economics, Queen’s University, Dunning Hall 209, 94 University Avenue, Kingston, Ontario K7L 3N6, Canada; e-mail: [email protected].
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Abstract

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

Type
MISCELLANEA
Information
Econometric Theory , Volume 36 , Issue 4 , August 2020 , pp. 751 - 772
Copyright
© Cambridge University Press 2019

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Footnotes

We are grateful to the Co-Editor, Rob Taylor, three anonymous referees, Søren Johansen, Peter M. Robinson, and seminar participants at Universidad Carlos III, Universitat Pompeu Fabra, Universidad de Alicante, University of Nottingham, and at the 3rd CREATES Long Memory Symposium for useful comments. Javier Hualde’s research is supported by the Spanish Ministerio de Economía y Competitividad through project ECO2015-64330-P. Morten Ø. Nielsen’s research is supported by the Canada Research Chairs program and the Social Sciences and Humanities Research Council of Canada (SSHRC). Both authors are thankful to the Center for Research in Econometric Analysis of Time Series (CREATES, funded by the Danish National Research Foundation, DNRF78) for financial support.

References

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