How Big is Big Enough? Justifying Results of the iid Test Based on the Correlation Integral in the Non-Normal World
Kocenda (2001) introduced the test for nonlinear dependencies in time series data based on the correlation integral. The idea of the test is to estimate the correlation dimension by integrating over a range of proximity parameter epsilon. However, there is an unexplored avenue if one wants to use the test to identify nonlinear structure in nonnormal data. Using the Monte Carlo studies, we show that non-normality leads to an over-rejection of the null hypothesis due to two reasons: First, the data are not iid, and second, the data are non-normal. It is shown that even a very small deviation from normality could lead to a rejection of the null hypothesis and hence a wrong conclusion. Therefore, the bootstrap method is introduced and it is shown that it helps to avoid the over-rejection problem; moreover the power of the test increases by a significant amount. These findings help us to extend the use of the test into many other fields that deal with nonlinear data that are not necessarily normal, e. g. financial economics, stock price volatility, stock market efficiency, stock exchange, behavior of equity indices, nonlinear dynamics in foreign exchange rates, or interest rates.
|Date of creation:||Sep 2006|
|Date of revision:|
|Contact details of provider:|| Postal: P.O. Box 882, Politickych veznu 7, 111 21 Praha 1|
Phone: (+420) 224 005 123
Fax: (+420) 224 005 333
Web page: http://www.cerge-ei.cz
More information through EDIRC
References listed on IDEAS
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.:
- Evzen Kocenda & Lubos Briatka, 2004.
"Advancing the iid Test Based on Integration across the Correlation Integral: Ranges, Competition, and Power,"
CERGE-EI Working Papers
wp235, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
- Evzen Kocenda & Lubos Briatka, 2005. "Optimal Range for the iid Test Based on Integration Across the Correlation Integral," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 265-296.
- Evzen Kocenda & Lubos Briatka, 2004. "Advancing the iid Test Based on Integration across the Correlation Integral: Ranges, Competition, and Power," Econometrics 0409001, EconWPA.
- Bera, Anil K. & Jarque, Carlos M., 1982. "Model specification tests : A simultaneous approach," Journal of Econometrics, Elsevier, vol. 20(1), pages 59-82, October.
- Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997.
"A single-blind controlled competition among tests for nonlinearity and chaos,"
Journal of Econometrics,
Elsevier, vol. 82(1), pages 157-192.
- William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201219, University of Kansas, Department of Economics, revised Sep 2012.
- William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996. "A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos," Econometrics 9602005, EconWPA, revised 20 Sep 1996.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
- Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993.
"Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests,"
Journal of Econometrics,
Elsevier, vol. 56(3), pages 269-290, April.
- Tom Doan, . "REGRESET: RATS procedure to perform Ramsey RESET test on regression," Statistical Software Components RTS00181, Boston College Department of Economics.
- Tom Doan, . "REGWHITENNTEST: RATS procedure to perform White neural network test on regression," Statistical Software Components RTS00183, Boston College Department of Economics.
- Cecen, A. Aydin & Erkal, Cahit, 1996. "Distinguishing between stochastic and deterministic behavior in high frequency foreign exchange rate returns: Can non-linear dynamics help forecasting?," International Journal of Forecasting, Elsevier, vol. 12(4), pages 465-473, December.
- Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
- Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, EconWPA.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Russell Davidson & James MacKinnon, 2000.
"Bootstrap tests: how many bootstraps?,"
Taylor & Francis Journals, vol. 19(1), pages 55-68.
- Jorge Belaire-Franch, 2003. "A Note on Resampling the Integration Across the Correlation Integral with Alternative Ranges," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 337-349.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- Ashley, Richard A & Patterson, Douglas M, 1989. "Linear versus Nonlinear Macroeconomies: A Statistical Test," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 685-704, August.
When requesting a correction, please mention this item's handle: RePEc:cer:papers:wp308. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jana Koudelkova)
If references are entirely missing, you can add them using this form.