Asymptotic properties of the partition function and applications in tail index inference of heavy-tailed data

References

• U Frisch. Fully developed turbulence and intermittency. Ann N Y Acad Sci. 1980;357(1):359–367. doi: 10.1111/j.1749-6632.1980.tb29703.x
   Google Scholar
• BB Mandelbrot, AJ Fisher, LE Calvet. A multifractal model of asset returns. Cowles Foundation for Research in Economics, Yale University; 1997. Cowles Foundation Discussion Papers 1164.
   Google Scholar
• B Mandelbrot. The variation of certain speculative prices. J Bus. 1963;36(4):394–419. doi: 10.1086/294632
   Web of Science ®Google Scholar
• CC Heyde, N Leonenko. Student processes. Adv in Appl Probab. 2005;37(2):342–365. doi: 10.1239/aap/1118858629
   Web of Science ®Google Scholar
• M Meerschaert, H Scheffler. A simple robust estimation method for the thickness of heavy tails. J Statist Plann Inference. 1998;71(1):19–34. doi: 10.1016/S0378-3758(98)00093-7
   Web of Science ®Google Scholar
• A Sly, Self-similarity, multifractionality and miltifractality [MPhil thesis]. Australian National University; 2005.
   Google Scholar
• CC Heyde. Scaling issues for risky asset modelling. Math Methods Oper Res. 2009;69(3):593–603. doi: 10.1007/s00186-008-0253-6
   Web of Science ®Google Scholar
• C Heyde, A Sly. A cautionary note on modeling with fractional Lévy flights. Phys A. 2008;387(21):5024–5032. doi: 10.1016/j.physa.2008.05.029
   Web of Science ®Google Scholar
• B Hill. A simple general approach to inference about the tail of a distribution. Ann Statist. 1975;3(5):1163–1174. doi: 10.1214/aos/1176343247
   Web of Science ®Google Scholar
• P Embrechts, C Klüppelberg, T Mikosch. Modelling extremal events: for insurance and finance. Vol. 33. Berlin: Springer; 1997.
   Google Scholar
• L De Haan, A Ferreira. Extreme value theory: an introduction. Berlin: Springer; 2006.
   Google Scholar
• M Meerschaert, H Scheffler. Nonparametric methods for heavy tailed vector data: a survey with applications from finance and hydrology. In: Akritas MG, Politis DN, editors. Recent advances and trends in nonparametric statistics. Amsterdam: Elsevier; 2003. p. 265–279.
   Google Scholar
• JL Doob. The Brownian movement and stochastic equations. Ann Math. 1942;43(2):351–369. doi: 10.2307/1968873
   Google Scholar
• A Janicki, A Weron. Simulation and chaotic behavior of alpha-stable stochastic processes. Hugo Steinhaus Center, Wroclaw University of Technology; 1994.
   Google Scholar
• E Taufer, NN Leonenko. Simulation of Lèvy-driven Ornstein–Uhlenbeck processes with given marginal distribution. Comput Statist Data Anal. 2009;53(6):2427–2437. doi: 10.1016/j.csda.2008.02.026
   Web of Science ®Google Scholar
• H Masuda. On multidimensional Ornstein–Uhlenbeck processes driven by a general Lévy process. Bernoulli. 2004;10(1):97–120. doi: 10.3150/bj/1077544605
   Web of Science ®Google Scholar
• BM Bibby, IM Skovgaard, M Sørensen. Diffusion-type models with given marginal distribution and autocorrelation function. Bernoulli. 2005;19(2):191–220. doi: 10.3150/bj/1116340291
   Google Scholar
• NN, Šuvak N Leonenko. Statistical inference for Student diffusion process. Stoch Anal Appl. 2010;28(6):972–1002. doi: 10.1080/07362994.2010.515476
   Web of Science ®Google Scholar
• SM Iacus, Simulation and inference for stochastic differential equations: with R examples, Springer Series in Statistics, Vol. XVIII. New York, Heidelberg, Berlin: Springer; 2008.
   Google Scholar
• H Rootzén, M Leadbetter, L De Haan. Tail and quantile estimation for strongly mixing stationary sequences. DTIC Document; 1990. Tech Rep.
   Google Scholar
• AL Dekkers, JH Einmahl, L De Haan. A moment estimator for the index of an extreme-value distribution. Ann Statist. 1989;17(4):1833–1855.
   Web of Science ®Google Scholar
• J Beirlant, Y Goegebeur, J Segers, J Teugels. Statistics of extremes: theory and applications. New York: Wiley; 2006.
   Google Scholar
• SI Resnick. Heavy tail modeling and teletraffic data: special invited paper. Ann Statist. 1997;25(5):1805–1869. doi: 10.1214/aos/1069362376
   Web of Science ®Google Scholar
• M Kratz, SI Resnick. The QQ-estimator and heavy tails. Stoch Models. 1996;12(4):699–724. doi: 10.1080/15326349608807407
   Google Scholar
• P Doukhan. Mixing: properties and examples. Vol. 85. New York: Springer-Verlag; 1994.
   Google Scholar
• E Rio. Inequalities and limit theorems for weakly dependent sequences. English translation of: ‘Théorie asymptotique des processus aléatoires faiblement dépendants’; 2013.
   Google Scholar
• P Hall, CC Heyde. Martingale limit theory and its application. New York: Academic Press; 1980.
   Google Scholar
• MR Leadbetter, G Lindgren, H Rootzén. Extremes and related properties of random sequences and processes. Berlin: Springer; 1982.
   Google Scholar