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How Big is Big Enough? Justifying Results of the iid Test Based on the Correlation Integral in the Non-Normal World

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  • Lubos Briatka
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    Abstract

    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.

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    Bibliographic Info

    Paper provided by The Center for Economic Research and Graduate Education - Economic Institute, Prague in its series CERGE-EI Working Papers with number wp308.

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    Date of creation: Sep 2006
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    Handle: RePEc:cer:papers:wp308

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    Keywords: Chaos; nonlinear dynamics; correlation integral; Monte Carlo; power tests; high-frequency economic and financial data;

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    1. 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.
    2. 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.
    3. 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.
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    7. 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.
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    9. 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.
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    13. 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 - Economic Institute, Prague.
    14. 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.
    15. 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.
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