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The Angular Distribution of Asset Returns in Delay Space


  • Roger Koppl

    (Fairleigh Dickinson University)

  • Carlo Nardone



We develop and apply a set of hypothesis tests with which to study changes in the angular distribution of points in delay space. Crack and Ledoit (1996) plotted daily stock returns against themselves with one day's lag. The graph shows these points collected along several rays from the origin. They correctly attribute this ``compass rose'' pattern to discreteness in the data. Our testing procedures allow one to test for changes in Crack and Ledoit's compass rose pattern. Our case study gives an example of such a change in distribution being caused by a change in regime. We plot the number of points along a given ray of the compass rose against the angle of that ray. This creates a ``theta histogram'' which describes the angular distribution of the points in delay space. We compare this distribution to a standard theta histogram created by a simple bootstrap procedure. We apply our technique to an important episode of Russian monetary history. Generally, the finance ministry actively intervened to influence the ruble exchange rate. The one exception was during Nicolai Bunge's tenure as finance minister. Bunge's successor, Ivan Vyshnegradsky, was an unusually vigorous interventionist. Hypothesis tests support the view that Vyshnegradsky's activism caused a disproportionate number of points of the compass rose to accumulate on the main diagonals in delay space.

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  • Roger Koppl & Carlo Nardone, 1997. "The Angular Distribution of Asset Returns in Delay Space," Finance 9703001, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:9703001
    Note: Type of Document - Postscript; prepared on UNIX LaTeX; to print on PostScript A4; pages: 27 ; figures: included. 10 figures

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    References listed on IDEAS

    1. Ahmed, Ehsan & Koppl, Roger & Rosser, J. Jr. & White, Mark V., 1997. "Complex bubble persistence in closed-end country funds," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 19-37, January.
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    Cited by:

    1. Mulligan, Robert F. & Koppl, Roger, 2011. "Monetary policy regimes in macroeconomic data: An application of fractal analysis," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(2), pages 201-211, May.
    2. Mário Gómez, 2009. "Risk, Uncertainty and Expectation as language game categories: - what we can still learn from Keynes," Working Papers Department of Economics 2009/14, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    3. Koppl, Roger & Whitman, Douglas Glen, 2004. "Rational-choice hermeneutics," Journal of Economic Behavior & Organization, Elsevier, vol. 55(3), pages 295-317, November.
    4. Mulligan, Robert F., 2004. "Fractal analysis of highly volatile markets: an application to technology equities," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(1), pages 155-179, February.
    5. Koppl, Roger G., 1996. "It is high time we take our ignorance more seriously," International Review of Financial Analysis, Elsevier, vol. 5(3), pages 259-272.
    6. Mulligan, Robert F. & Lombardo, Gary A., 2004. "Maritime businesses: volatile stock prices and market valuation inefficiencies," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 321-336, May.
    7. Butos William Ν. & Koppl Roger, 1999. "Hayek And Kirzner At The Keynesian Beauty Contest," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 9(2-3), pages 1-20, June.

    More about this item


    returns distribution delay bootstrap ruble;

    JEL classification:

    • G - Financial Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs


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