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Stochastic processes, non-normal innovations, and the use of scaling ratios

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  • Groenendijk, Patrick A.

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Lucas, André
  • Vries, Casper G. de

Abstract

Market efficiency tests that rely on the martingale difference be-havior of returns can be based on various volatility measures. This paper argues that, to be able to differentiate between dependence and fat-tailedness. one should look simultaneously at plots based on ab-solute returns and variances. If the distribution is heavy-tailed, this shows up in the absolute moment plots, but not in the variance re-lated plots. Linear dependence. by contrast, is revealed in both plots. We provide and discuss an analytical and a simulation experiment illustrating these points.

Suggested Citation

  • Groenendijk, Patrick A. & Lucas, André & Vries, Casper G. de, 1997. "Stochastic processes, non-normal innovations, and the use of scaling ratios," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    • Handle: RePEc:vua:wpaper:1997-58
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    File URL: http://degree.ubvu.vu.nl/repec/vua/wpaper/pdf/19970058.pdf
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    References listed on IDEAS

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    1. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    2. Lo, Andrew W. & MacKinlay, A. Craig, 1989. "The size and power of the variance ratio test in finite samples : A Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 40(2), pages 203-238, February.
    3. Richardson, Matthew & Stock, James H., 1989. "Drawing inferences from statistics based on multiyear asset returns," Journal of Financial Economics, Elsevier, vol. 25(2), pages 323-348, December.
    4. Liu, Christina Y & He, Jia, 1991. "A Variance-Ratio Test of Random Walks in Foreign Exchange Rates," Journal of Finance, American Finance Association, vol. 46(2), pages 773-785, June.
    5. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    6. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
    7. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
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    Cited by:

    1. Patrick A. Groenendijk & André Lucas & Casper G. de Vries, 1998. "A Hybrid Joint Moment Ratio Test for Financial Time Series," Tinbergen Institute Discussion Papers 98-104/2, Tinbergen Institute.
    2. Dacorogna, Michel & Elbahtouri, Laila & Kratz, Marie, 2015. "Explicit diversifiction benefit for dependent risks," ESSEC Working Papers WP1522, ESSEC Research Center, ESSEC Business School.

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    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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