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A New Regression-Based Tail Index Estimator: An Application to Exchange Rates

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  • Paulo M.M. Rodrigues
  • João Nicolau

Abstract

In this paper, a new regression-based approach for the estimation of the tail index of heavy-tailed distributions is introduced. Comparatively to many procedures currently available in the literature, our method does not involve order statistics and can be applied in more general contexts than just Pareto. The procedure is in line with approaches used in experimental data analysis with fixed explanatory variables, and has several important features which are worth highlighting. First, it provides a bias reduction when compared to available regression-based methods and a fortiori over standard least-squares based estimators of the tail index. Second, it is more resilient to the choice of the tail length used in the estimation of the index than the widely used Hill estimator. Third, when the effect of the slowly varying function at infinity of the Pareto distribution (the so called second order behaviour of the Taylor expansion) vanishes slowly our estimator continues to perform satisfactorily, whereas the Hill estimator rapidly deteriorates. Fourth, our estimator performs well under dependence of unknown form. For inference purposes, we also provide a way to compute the asymptotic variance of the proposed estimator under time dependence and conditional heteroscedasticity. An empirical application of the procedure to exchange rates is also provided.

Suggested Citation

  • Paulo M.M. Rodrigues & João Nicolau, 2015. "A New Regression-Based Tail Index Estimator: An Application to Exchange Rates," Working Papers w201514, Banco de Portugal, Economics and Research Department.
  • Handle: RePEc:ptu:wpaper:w201514
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    References listed on IDEAS

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    1. Frankel, Jeffrey A. & Fajnzylber, Eduardo & Schmukler, Sergio L. & Serven, Luis, 2001. "Verifying exchange rate regimes," Journal of Development Economics, Elsevier, vol. 66(2), pages 351-386, December.
    2. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    3. Patnaik, Ila & Shah, Ajay & Sethy, Anmol & Balasubramaniam, Vimal, 2011. "The exchange rate regime in Asia: From crisis to crisis," International Review of Economics & Finance, Elsevier, vol. 20(1), pages 32-43, January.
    4. Andrew K. Rose, 2011. "Exchange Rate Regimes in the Modern Era : Fixed, Floating, and Flaky," Journal of Economic Literature, American Economic Association, vol. 49(3), pages 652-672, September.
    5. Carmen M. Reinhart & Kenneth S. Rogoff, 2004. "The Modern History of Exchange Rate Arrangements: A Reinterpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 1-48.
    6. Koedijk, Kees G. & Stork, Philip A. & de Vries, Casper G., 1992. "Differences between foreign exchange rate regimes: The view from the tails," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 462-473, October.
    7. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    8. Ibragimov Marat & Khamidov Rufat, 2010. "Heavy-Tailedness and Volatility in Emerging Foreign Exchange Markets: Theory and Empirics," EERC Working Paper Series 10/06e, EERC Research Network, Russia and CIS.
    9. Hartmann, P. & Straetmans, S. & de Vries, C.G., 2010. "Heavy tails and currency crises," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 241-254, March.
    10. Wang, Jianxin & Yang, Minxian, 2009. "Asymmetric volatility in the foreign exchange markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(4), pages 597-615, October.
    11. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    12. Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716, October.
    13. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    14. Hill, Jonathan B., 2010. "On Tail Index Estimation For Dependent, Heterogeneous Data," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1398-1436, October.
    15. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
    16. Mark E. Crovella & Murad S. Taqqu, 1999. "Estimating the Heavy Tail Index from Scaling Properties," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 55-79, July.
    17. Bollerslev, Tim & Domowitz, Ian, 1993. "Trading Patterns and Prices in the Interbank Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 48(4), pages 1421-1443, September.
    18. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    19. Xavier Gabaix & Rustam Ibragimov, 2006. "Log(Rank-1/2): A Simple Way to Improve the OLS Estimation of Tail Exponents," Harvard Institute of Economic Research Working Papers 2106, Harvard - Institute of Economic Research.
    20. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    21. Ibragimov, Marat & Ibragimov, Rustam & Kattuman, Paul, 2013. "Emerging markets and heavy tails," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2546-2559.
    22. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    23. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    24. Hols, Martien C A B & de Vries, Casper G, 1991. "The Limiting Distribution of Extremal Exchange Rate Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 287-302, July-Sept.
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    Cited by:

    1. João Nicolau & Paulo M. M. Rodrigues, 2019. "A New Regression-Based Tail Index Estimator," The Review of Economics and Statistics, MIT Press, vol. 101(4), pages 667-680, October.
    2. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Heavy tails and asymmetry of returns in the Russian stock market," Emerging Markets Review, Elsevier, vol. 32(C), pages 200-219.

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