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Weak convergence to the t-distribution


  • Christian Schluter
  • Mark Trede


We present a new limit theorem for random means: if the sample size is not deterministic but has a negative binomial or geometric distribution, the limit distribution of the normalised random mean is a t-distribution with degrees of freedom depending on the shape parameter of the negative binomial distribution. Thus the limit distribution exhibits exhibits heavy tails, whereas limit laws for random sums do not achieve this unless the summands have in nite variance. The limit law may help explain several empirical regularities. We consider two such examples: rst, a simple model is used to explain why city size growth rates are approximately t-distributed. Second, a random averaging argument can account for the heavy tails of high-frequency returns. Our empirical investigations demonstrate that these predictions are borne out by the data.

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  • Christian Schluter & Mark Trede, 2011. "Weak convergence to the t-distribution," CQE Working Papers 2111, Center for Quantitative Economics (CQE), University of Muenster.
  • Handle: RePEc:cqe:wpaper:2111

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    References listed on IDEAS

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    12. Wilfling, Bernd & Maennig, Wolfgang, 2001. "Exchange rate dynamics in anticipation of time-contingent regime switching: modelling the effects of a possible delay," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 91-113, February.
    13. Sutherland, Alan, 1995. "State- and time-contingent switches of exchange rate regime," Journal of International Economics, Elsevier, vol. 38(3-4), pages 361-374, May.
    14. De Grauwe, Paul & Dewachter, Hans & Veestraeten, Dirk, 1999. "Price dynamics under stochastic process switching: some extensions and an application to EMU1," Journal of International Money and Finance, Elsevier, vol. 18(2), pages 195-224, February.
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    16. Willard, Kristen L & Guinnane, Timothy W & Rosen, Harvey S, 1996. "Turning Points in the Civil War: Views from the Greenback Market," American Economic Review, American Economic Association, vol. 86(4), pages 1001-1018, September.
    17. Milton Friedman & Anna J. Schwartz, 1963. "A Monetary History of the United States, 1867–1960," NBER Books, National Bureau of Economic Research, Inc, number frie63-1, January.
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    convergence; t-distribution; limit theorem;

    JEL classification:

    • A - General Economics and Teaching

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