Properties of nonlinear transformations of fractionally integrated processes
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 110 (2002)
Issue (Month): 2 (October)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- Dittmann, Ingolf & Granger, Clive W.J., 2000. "Properties of Nonlinear Transformations of Fractionally Integrated Processes," University of California at San Diego, Economics Working Paper Series qt0kk9x0mc, Department of Economics, UC San Diego.
- Dittmann, Ingolf & Granger, Clive W. J., 2000. "Properties of nonlinear transformations of fractionally integrated processes," Technical Reports 2000,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Diebold, Francis X. & Inoue, Atsushi, 2001.
"Long memory and regime switching,"
Journal of Econometrics,
Elsevier, vol. 105(1), pages 131-159, November.
- Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
- Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004.
"Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies,"
CIRANO Working Papers
- 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.
- Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," NBER Working Papers 10914, National Bureau of Economic Research, Inc.
- 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.
- Bhardwaj, Geetesh & Swanson, Norman R., 2006. "An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 539-578.
- 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.
- Marco Avarucci & Domenico Marinucci, 2005.
"Polynomial Cointegration Among Stationary Processes With Long Memory,"
Economics Working Papers
we055123, Universidad Carlos III, Departamento de Economía.
- Avarucci, Marco & Marinucci, Domenico, . "Polynomial cointegration among stationary processes with long memory," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/351, Universidad Carlos III de Madrid.
- Gabriele La Spada & Fabrizio Lillo, 2011. "The effect of round-off error on long memory processes," Papers 1107.4476, arXiv.org, revised Mar 2013.
- 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.
- Heejoon Han & Dennis Kristensen, 2013.
"Asymptotic theory for the QMLE in GARCH-X models with stationary and non-stationary covariates,"
CeMMAP working papers
CWP18/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- 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.
- 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.
- Haldrup, Niels & Nielsen, Morten Oe., . "Estimation of Fractional Integration in the Presence of Data Noise," Economics Working Papers 2003-10, School of Economics and Management, University of Aarhus.
- 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.
- 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.
- Yoon, Gawon, 2005. "Long-memory property of nonlinear transformations of break processes," Economics Letters, Elsevier, vol. 87(3), pages 373-377, June.
- Wang, Yudong & Wu, Chongfeng, 2012. "Long memory in energy futures markets: Further evidence," Resources Policy, Elsevier, vol. 37(3), pages 261-272.
- 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.
- repec:eui:euidis:urn:hdl:1814/5025 is not listed on IDEAS
- Dominique Guegan, 2005. "How can we define the concept of long memory ? An econometric survey," Post-Print halshs-00179343, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.