{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T21:31:35Z","timestamp":1774906295965,"version":"3.50.1"},"reference-count":42,"publisher":"MIT Press - Journals","issue":"4","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2019,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A new regression-based approach for the estimation of the tail index of heavy-tailed distributions with several important properties is introduced. First, it provides a bias reduction when compared to available regression-based methods; second, it is resilient to the choice of the tail length used for the estimation of the tail index; third, when the effect of the slowly varying function at infinity of the Pareto distribution vanishes slowly, it continues to perform satisfactorily; and fourth, it performs well under dependence of unknown form. An approach to compute the asymptotic variance under time dependence and conditional heteroskcedasticity is also provided.<\/jats:p>","DOI":"10.1162\/rest_a_00768","type":"journal-article","created":{"date-parts":[[2018,11,3]],"date-time":"2018-11-03T01:18:40Z","timestamp":1541207920000},"page":"667-680","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":11,"title":["A New Regression-Based Tail Index Estimator"],"prefix":"10.1162","volume":"101","author":[{"given":"Jo\u00e3o","family":"Nicolau","sequence":"first","affiliation":[{"name":"ISEG-Universidade de Lisboa and REM\/CEMAPRE"}]},{"given":"Paulo M. M.","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Banco de Portugal and NovaSBE, Universidade Nova de Lisboa"}]}],"member":"281","published-online":{"date-parts":[[2019,10,1]]},"reference":[{"key":"2021051417213863200_B1","doi-asserted-by":"crossref","unstructured":"Andrews, D. W. K., and J. C.Monahan, \u201cAn Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator,\u201d Econometrica60 (1992), 953\u2013966.","DOI":"10.2307\/2951574"},{"key":"2021051417213863200_B2","doi-asserted-by":"crossref","unstructured":"Beirlant, J., Y.Goegebeur, J.Segers, J.Teugels, D.Waal, and C.Ferro, Statistics of Extremes: Theory and Applications (Hoboken, NJ: John Wiley, 2004).","DOI":"10.1002\/0470012382"},{"key":"2021051417213863200_B3","doi-asserted-by":"crossref","unstructured":"Beirlant, J., C.Bouquiaux, and B.Werker, \u201cSemiparametric Lower Bounds for Tail Index Estimation,\u201d Journal of Statistical Planning and Inference136:3 (2006), 705\u2013729.","DOI":"10.1016\/j.jspi.2004.08.018"},{"key":"2021051417213863200_B4","doi-asserted-by":"crossref","unstructured":"Beirlant, J., P.Vynckier, and J. L.Teugels, \u201cTail Index Estimation, Pareto Quantile Plots, and Regression Diagnostics,\u201d Journal of the American Statistical Association91 (1996), 1659\u20131667.","DOI":"10.1080\/01621459.1996.10476735"},{"key":"2021051417213863200_B5","doi-asserted-by":"crossref","unstructured":"Danielsson, J., L.de Haan, L.Peng, and C. G.de Vries, \u201cUsing a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation,\u201d Journal of Multivariate Analysis76 (2001), 226\u2013248.","DOI":"10.1006\/jmva.2000.1903"},{"key":"2021051417213863200_B6","doi-asserted-by":"crossref","unstructured":"Drees, H., L.de Haan, and S.Resnick, \u201cHow to Make a Hill Plot,\u201d Annals Statistics28 (2000), 254\u2013274.","DOI":"10.1214\/aos\/1016120372"},{"key":"2021051417213863200_B7","unstructured":"Embrechts, P., C.Kl\u00fcppelberg, and T.Mikosch, Modeling Extremal Events for Insurance and Finance (Berlin: Springer, 2012)."},{"key":"2021051417213863200_B8","doi-asserted-by":"crossref","unstructured":"Gabaix, X.\n          , \u201cZipf's Law for Cities: An Explanation,\u201d Quarterly Journal of Economics114 (1999), 739\u2013767.","DOI":"10.1162\/003355399556133"},{"key":"2021051417213863200_B9","doi-asserted-by":"crossref","unstructured":"Gabaix, X.\n           \u201cPower Laws in Economics and Finance,\u201d Annual Review of Economics1 (2009), 255\u2013293.","DOI":"10.1146\/annurev.economics.050708.142940"},{"key":"2021051417213863200_B10","doi-asserted-by":"crossref","unstructured":"Gabaix, X., P.Gopikrishnan, V.Plerou, and H. E.Stanley, \u201cA Theory of Power Law Distributions in Financial Market Fluctuations,\u201d Nature423 (2003), 267\u2013270.","DOI":"10.1038\/nature01624"},{"key":"2021051417213863200_B11","doi-asserted-by":"crossref","unstructured":"Gabaix, X., P.Gopikrishnan, V.Plerou, and H. E.Stanley, \u201cInstitutional Investors and Stock Market Volatility,\u201d Quarterly Journal of Economics121 (2006), 461\u2013504.","DOI":"10.1162\/qjec.2006.121.2.461"},{"key":"2021051417213863200_B12","doi-asserted-by":"crossref","unstructured":"Gabaix, X., and R.Ibragimov, \u201cLog(Rank-1\/2): A Simple Way to Improve the OLS Estimation of Tail Exponents,\u201d Journal of Business Economics and Statistics29:1 (2012), 24\u201339.","DOI":"10.1198\/jbes.2009.06157"},{"key":"2021051417213863200_B13","doi-asserted-by":"crossref","unstructured":"Gabaix, X., and Y. M.Ioannides, \u201cThe Evolution of City Size Distributions,\u201d in V.Handerson and J. F.Thisse, eds., Handbook of Urban and Regional Economics (Amsterdam: Elsevier, North-Holland, 2004).","DOI":"10.1016\/S1574-0080(04)80010-5"},{"key":"2021051417213863200_B14","doi-asserted-by":"crossref","unstructured":"Gabaix, X., and M.Maggiori, \u201cInternational Liquidity and Exchange Rate Dynamics,\u201d Quarterly Journal of Economics130:3 (2015), 1369\u20131420.","DOI":"10.1093\/qje\/qjv016"},{"key":"2021051417213863200_B15","doi-asserted-by":"crossref","unstructured":"Hall, P.\n          , \u201cOn Some Simple Estimates of an Exponent of Regular Variation,\u201d Journal of the Royal Statistical Association (Series B) 44 (1982), 37\u201342.","DOI":"10.1111\/j.2517-6161.1982.tb01183.x"},{"key":"2021051417213863200_B16","doi-asserted-by":"crossref","unstructured":"Hartmann, P., S.Straetmans, and C. G.de Vries, \u201cHeavy Tails and Currency Crises,\u201d Journal of Empirical Finance17:2 (2010), 241\u2013254.","DOI":"10.1016\/j.jempfin.2009.09.004"},{"key":"2021051417213863200_B17","doi-asserted-by":"crossref","unstructured":"Hill, B. M.\n          , \u201cA Simple General Approach to Inference about the Tail of a Distribution,\u201d Annals of Statistics3 (1975), 1163\u20131174.","DOI":"10.1214\/aos\/1176343247"},{"key":"2021051417213863200_B18","doi-asserted-by":"crossref","unstructured":"Hill, J. B.\n          , \u201cOn Tail Index Estimation for Dependent, Heterogeneous Data,\u201d Econometric Theory26 (2010), 1398\u20131436.","DOI":"10.1017\/S0266466609990624"},{"key":"2021051417213863200_B19","doi-asserted-by":"crossref","unstructured":"Hols, M. C. A., and C. G.de Vries, \u201cThe Limiting Distribution of Extremal Exchange Rate Returns,\u201d Journal of Applied Econometrics6:3 (1991), 287\u2013302.","DOI":"10.1002\/jae.3950060306"},{"key":"2021051417213863200_B20","doi-asserted-by":"crossref","unstructured":"Huisman, R., K. G.Koedijk, C. J. M.Kool, and F.Palm, \u201cTail-Index Estimates in Small Samples,\u201d Journal of Business and Economic Statistics19 (2001), 208\u2013216.","DOI":"10.1198\/073500101316970421"},{"key":"2021051417213863200_B21","unstructured":"Ibragimov\n              M.\n            , Z.Davidova, and R.Khamidov, Heavy-Tailedness and Volatility in Emerging Foreign Exchange Markets: Theory and Empirics (Kiev: EERC, 2010)."},{"key":"2021051417213863200_B22","doi-asserted-by":"crossref","unstructured":"Ibragimov, M., R.Ibragimov, and P.Kattuman, \u201cEmerging Markets and Heavy Tails,\u201d Journal of Banking and Finance37:7 (2013), 2546\u20132559.","DOI":"10.1016\/j.jbankfin.2013.02.019"},{"key":"2021051417213863200_B23","unstructured":"Ibragimov, M., R.Ibragimov, and R.Khamidov, Measuring Inequality in CIS Countries: Theory and Empirics, GDN, working paper54 (2011)."},{"key":"2021051417213863200_B24","doi-asserted-by":"crossref","unstructured":"Ibragimov, M., R.Ibragimov, and J.Walden, Heavy-Tailed Distributions and Robustness in Economics and Finance (Berlin: Springer, 2015).","DOI":"10.1007\/978-3-319-16877-7"},{"key":"2021051417213863200_B25","doi-asserted-by":"crossref","unstructured":"Jansen, D., and C. G. deVries, \u201cOn the frequency of Large Stock Returns: Putting Booms and Busts into Perspective,\u201d this review73 (1991), 18\u201324.","DOI":"10.2307\/2109682"},{"key":"2021051417213863200_B26","doi-asserted-by":"crossref","unstructured":"Kearns, P., and A.Pagan, \u201cEstimating the Density Tail Index for Financial Time Series,\u201d this review79 (1997), 171\u2013175.","DOI":"10.1162\/003465397556755"},{"key":"2021051417213863200_B27","doi-asserted-by":"crossref","unstructured":"Koedijk, K. G., P. A.Stork, and C. G.de Vries, \u201cDifferences between Foreign Exchange Rate Regimes: The View from the Tails,\u201d Journal of International Money and Finance11 (1992), 462\u2013473.","DOI":"10.1016\/0261-5606(92)90012-M"},{"key":"2021051417213863200_B28","unstructured":"Kohler, M.\n          , \u201cExchange Rates during Financial Crises,\u201d BIS Quarterly Review (March 2010), 39\u201350."},{"key":"2021051417213863200_B29","doi-asserted-by":"crossref","unstructured":"Kratz, M., and S. I.Resnick, \u201cThe qq-Estimator and Heavy Tails,\u201d Stochastic Models12 (1996), 699\u2013724.","DOI":"10.1080\/15326349608807407"},{"key":"2021051417213863200_B30","doi-asserted-by":"crossref","unstructured":"Loretan, M., and P. C. B.Phillips, \u201cTesting the Covariance Stationarity of Heavy-Tailed Time Series,\u201d Journal of Empirical Finance1 (1994), 211\u2013248.","DOI":"10.1016\/0927-5398(94)90004-3"},{"key":"2021051417213863200_B31","doi-asserted-by":"crossref","unstructured":"Mason, D.\n          , \u201cLaws of Large Numbers for Sums of Extreme Values,\u201d Annals of Probability10 (1982), 754\u2013764.","DOI":"10.1214\/aop\/1176993783"},{"key":"2021051417213863200_B32","doi-asserted-by":"crossref","unstructured":"Mikosch, T., and C.St\u0103ric\u0103, \u201cLimit Theory for the Sample Autocorrelations and Extremes of a GARCH(1,1) Process,\u201d Annals of Statistics28 (2000), 1427\u20131451.","DOI":"10.1214\/aos\/1015957401"},{"key":"2021051417213863200_B33","unstructured":"Mohanty, M., and B.Berger, \u201cCentral Bank Views on Foreign Exchange Intervention,\u201d Bank for International Settlements paper73 (2013)."},{"key":"2021051417213863200_B34","doi-asserted-by":"crossref","unstructured":"Nguyen, T., and G.Samorodnitsky, \u201cTail Inference: Where Does the Tail Begin?\u201d Extremes15:4 (2012), 437\u2013461.","DOI":"10.1007\/s10687-011-0145-7"},{"key":"2021051417213863200_B35","unstructured":"Nicolau, J., and P. M. M.Rodrigues, \u201cA New Regression-Based Tail Index Estimator: An Application to Exchange Rates,\u201d Bank of Portugal working paper14 (2015)."},{"key":"2021051417213863200_B36","doi-asserted-by":"crossref","unstructured":"Reinhart, C. M., and K. S.Rogoff, \u201cThe Modern History of Exchange Rate Arrangements: A Reinterpretation,\u201d Quarterly Journal of Economics119:1 (2004), 1\u201348.","DOI":"10.1162\/003355304772839515"},{"key":"2021051417213863200_B37","doi-asserted-by":"crossref","unstructured":"Resnick, S., and C.St\u0103ric\u0103, \u201cSmoothing the Hill Estimator,\u201d Applied Probability29 (1997), 271\u2013293.","DOI":"10.2307\/1427870"},{"key":"2021051417213863200_B38","doi-asserted-by":"crossref","unstructured":"Rosen, K. T., and M.Resnick, \u201cThe Size Distribution of Cities: An Explanation of the Pareto Law and Primacy,\u201d Journal of Urban Economics8 (1980), 165\u2013186.","DOI":"10.1016\/0094-1190(80)90043-1"},{"key":"2021051417213863200_B39","unstructured":"Samorodnitsky, G., and M. S.Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (New York: Chapman and Hall, 1994)."},{"key":"2021051417213863200_B40","doi-asserted-by":"crossref","unstructured":"Stelzer, R.\n          , \u201cOn Markov-Switching ARMA Processes: Stationarity, Existence of Moments and Geometric Ergodicity,\u201d Econometric Theory25:1 (2009), 43\u201362.","DOI":"10.1017\/S0266466608090026"},{"key":"2021051417213863200_B41","doi-asserted-by":"crossref","unstructured":"Stoev, S. A., and G.Michailidis, \u201cOn the Estimation of the Heavy-Tail Exponent in Time Series Using the Max-Spectrum,\u201d Applied Stochastic Models in Business and Industry26:3 (2010), 224\u2013253.","DOI":"10.1002\/asmb.764"},{"key":"2021051417213863200_B42","doi-asserted-by":"crossref","unstructured":"van der Vaart, A. W., and J. A.Wellner, Weak Convergence and Empirical Processes with Applications to Statistics (New York: Springer, 1996).","DOI":"10.1007\/978-1-4757-2545-2_3"}],"container-title":["The Review of Economics and Statistics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/direct.mit.edu\/rest\/article-pdf\/101\/4\/667\/1916572\/rest_a_00768.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/direct.mit.edu\/rest\/article-pdf\/101\/4\/667\/1916572\/rest_a_00768.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,14]],"date-time":"2021-05-14T17:24:51Z","timestamp":1621013091000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/rest\/article\/101\/4\/667\/58566\/A-New-Regression-Based-Tail-Index-Estimator"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,1]]},"references-count":42,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,1]]},"published-print":{"date-parts":[[2019,10,1]]}},"URL":"https:\/\/doi.org\/10.1162\/rest_a_00768","relation":{},"ISSN":["0034-6535","1530-9142"],"issn-type":[{"value":"0034-6535","type":"print"},{"value":"1530-9142","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2019,10]]},"published":{"date-parts":[[2019,10,1]]}}}