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Properties of Nonlinear Transformations of Fractionally Integrated Processes

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  • Dittmann, Ingolf
  • Granger, Clive W.J.

Abstract

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0). For non-stationary I(d) processes, every integer power transformation is non-stationary and exhibits a deterministic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.

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Bibliographic Info

Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt0kk9x0mc.

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Date of creation: 01 Apr 2000
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Handle: RePEc:cdl:ucsdec:qt0kk9x0mc

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Keywords: nonlinear transformations; frationally integrated process;

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References

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  1. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  2. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
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Citations

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Cited by:
  1. Heejoon Han & Dennis Kristensen, 2012. "Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates," CREATES Research Papers 2012-25, School of Economics and Management, University of Aarhus.
  2. Zhang, Ting & Ho, Hwai-Chung & Wendler, Martin & Wu, Wei Biao, 2013. "Block sampling under strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2323-2339.
  3. Marzio Galeotti & Matteo Manera & Alessandro Lanza, 2009. "On the Robustness of Robustness Checks of the Environmental Kuznets Curve Hypothesis," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 42(4), pages 551-574, April.
  4. Geetesh Bhardwaj & Norman Swanson, 2004. "An Empirical Investigation of the Usefulness of ARFIMA Models for Predicting Macroeconomic and Financial Time Series," Departmental Working Papers 200422, Rutgers University, Department of Economics.
  5. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
  6. Guégan D., 2004. "How Can We Define The Concept of Long Memory? An Econometric Survey," School of Economics and Finance Discussion Papers and Working Papers Series 178, School of Economics and Finance, Queensland University of Technology.
  7. McHale, I.G. & Peel, D.A., 2010. "Habit and long memory in UK lottery sales," Economics Letters, Elsevier, vol. 109(1), pages 7-10, October.
  8. Gabriele La Spada & Fabrizio Lillo, 2011. "The effect of round-off error on long memory processes," Papers 1107.4476, arXiv.org, revised Mar 2013.
  9. Ting Zhang & Hwai-Chung Ho & Martin Wendler & Wei Biao Wu, 2013. "Block Sampling under Strong Dependence," Papers 1312.5807, arXiv.org.
  10. Høg, Espen P. & Frederiksen, Per H., 2006. "The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application," Finance Research Group Working Papers F-2006-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  11. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
  12. Esben Hoeg & Per Frederiksen, 2006. "The Fractional OU Process: Term Structure Theory and Application," Computing in Economics and Finance 2006 194, Society for Computational Economics.
  13. Wang, Yudong & Wu, Chongfeng, 2012. "Long memory in energy futures markets: Further evidence," Resources Policy, Elsevier, vol. 37(3), pages 261-272.
  14. Azamo, Baudouin Tameze & Krämer, Walter, 2006. "Structural Change and long memory in the GARCH(1,1)-model," Technical Reports 2006,33, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  15. Yoon, Gawon, 2005. "Long-memory property of nonlinear transformations of break processes," Economics Letters, Elsevier, vol. 87(3), pages 373-377, June.
  16. Marco Avarucci & Domenico Marinucci, 2005. "Polynomial Cointegration Among Stationary Processes With Long Memory," Economics Working Papers we055123, Universidad Carlos III, Departamento de Economía.

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