The increment ratio statistic
AbstractWe introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series Xt, including short memory (d=0), (stationary) long-memory and unit roots (d=1). If Sn behaves asymptotically as an (integrated) fractional Brownian motion with parameter , the IR statistic converges to a monotone function [Lambda](d) of as both the sample size N and the window parameter m increase so that N/m-->[infinity]. For Gaussian observations Xt, we obtain a rate of decay of the bias EIR-[Lambda](d) and a central limit theorem , in the region . Graphs of the functions [Lambda](d) and [sigma](d) are included. A simulation study shows that the IR test for short memory (d=0) against stationary long-memory alternatives has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.
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 Multivariate Analysis.
Volume (Year): 99 (2008)
Issue (Month): 3 (March)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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.:
- GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, .
"Rescaled variance and related tests for long memory in volatility and levels,"
CORE Discussion Papers RP
-1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
- Francis X. Diebold & Atsushi Inoue, 2000.
"Long Memory and Regime Switching,"
NBER Technical Working Papers
0264, National Bureau of Economic Research, Inc.
- Perron, Pierre, 1989.
"The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,"
Econometric Society, vol. 57(6), pages 1361-1401, November.
- Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
- Csörgo, Sándor & Mielniczuk, Jan, 1995. "Distant long-range dependent sums and regression estimation," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 143-155, September.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991.
"Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?,"
Cowles Foundation Discussion Papers
979, Cowles Foundation for Research in Economics, Yale University.
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
- Tom Doan, . "KPSS: RATS procedure to perform KPSS (Kwiatowski, Phillips, Schmidt, and Shin) stationarity test," Statistical Software Components RTS00100, Boston College Department of Economics.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 475-95, July.
- Sibbertsen, Philipp, 2003.
"Log-periodogram estimation of the memory parameter of a long-memory process under trend,"
Statistics & Probability Letters,
Elsevier, vol. 61(3), pages 261-268, February.
- Sibbertsen, Philipp, 2001. "Log-periodogram estimation of the memory parameter of a long-memory process under trend," Technical Reports 2001,39, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
- Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
- Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(06), pages 989-1029, December.
- Lo, Andrew W, 1991.
"Long-Term Memory in Stock Market Prices,"
Econometric Society, vol. 59(5), pages 1279-313, September.
- Tom Doan, . "RSSTATISTIC: RATS procedure to compute R/S Statistic (classical or Lo's modified)," Statistical Software Components RTS00191, Boston College Department of Economics.
- Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
- J. Bardet & G. Lang & E. Moulines & P. Soulier, 2000. "Wavelet Estimator of Long-Range Dependent Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 85-99, January.
- Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
- Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
- Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 177-190, January.
- Lavielle, Marc, 1999. "Detection of multiple changes in a sequence of dependent variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 79-102, September.
- Bardet, Jean-Marc & Surgailis, Donatas, 2013. "Nonparametric estimation of the local Hurst function of multifractional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1004-1045.
- Yoon, Gawon, 2009. "Is high real interest rate persistence an intrinsic characteristic of industrialized economies?," Economic Modelling, Elsevier, vol. 26(2), pages 359-363, March.
- Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
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.