Parameter estimation for stable distributions with application to commodity futures log-returns

References

• Ament, S., & O’Neal, M. (2016). Accurate and efficient numerical calculation of stable densities via optimized quadrature and asymptotics. , arXiv: 1607.04247v1
   Google Scholar
• Applebaum, D. (2004). Lévy processes and stochastic calculus. Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press.
   Google Scholar
• Bachelier, L. (1900). Théorie de la spéculation. Annales scientifiques de l’É.N.S. 3e série, 17, 21–86.
   Google Scholar
• Chambers, J. M., Mallows, C. L., & Stuck, B. W. (1976). A method for simulating stable random variables. Journal of the American Statistical Association, 71, 340–344.
   Web of Science ®Google Scholar
• Dumouchel, W. H. (1971). Stable distributions in statistical inference. The Journal of the American Statistical Association, 78, 469–477.
   Google Scholar
• Fama, E. F. (1963). Mandelbrot and the stable paretian hypothesis. The Journal of Business, 36, 420–429.
   Web of Science ®Google Scholar
• Fama, E. F., & Roll, R. (1968). Some properties of symmetric stable distributions. Journal of the American Statistical Association, 63, 817–836.
   Web of Science ®Google Scholar
• Fama, E. F., & Roll, R. (1971). Parameter estimates for symmetric stable distributions. Journal of the American Statistical Association, 66, 331–338.
   Web of Science ®Google Scholar
• Holt, D. R., & Crow, E. L. (1973). Tables and graphs of the stable probability density function. Journal of Research of the National Bureau of Standards. Section D, 77, 143–198.
   Google Scholar
• Koutrouvelis, I. A. (1980). Regression-type estimation of the parameters of stable laws. Journal of the American Statistical Association, 75, 918–928.
   Web of Science ®Google Scholar
• Kuruoğlu, E. E. (2001). Density parameter estimation of skewed alpha-stable distributions. IEEE Transactions on signal processing, 49, 2192–2201.
   Web of Science ®Google Scholar
• Mandelbrot, B. (1959). Variables et processus stochastiques de pareto-Lévy et la répartition des revenus. Comptes Rendus de l’Académie des Sciences, 249, 2153–2155.
   Google Scholar
• Mandelbrot, B. (1962). Paretian distributions and income maximization. The Quarterly Journal of Economics, 76, 57–85.
   Web of Science ®Google Scholar
• Mandelbrot, B. (1963). The variation of certain speculative prices. The Journal of Business, 36, 394–419.
   Web of Science ®Google Scholar
• Ma, X. Y., & Nikias, C. L. (1995). Parameter estimation and blind channel identification in impulsive signal environments. IEEE Transactions on signal processing, 43, 2884–2897.
   Web of Science ®Google Scholar
• McCulloch, J. H. (1986). Simple consistent estimators of stable distribution parameters. Communications in Statistics - Simulation and Computation, 15, 1109–1136.
   Web of Science ®Google Scholar
• McCulloch, J. H. (1996). 13 financial applications of stable distributions. Statistical Methods in Finance, 14, 393–425.
   Google Scholar
• Mittnik, S., Rachev, S. T., Doganoglu, T., & Chenyao, D. (1999). Maximum likelihood estimation of stable paretian models. Mathematical and Computer Modelling, 9, 275–293.
   Google Scholar
• Nolan, J. P. (1997). Numerical calculation of stable densities and distribution functions. Communications in Statistics, Stochastic Models, 13, 795–774.
   Google Scholar
• Nolan, J. P. (2001). Maximum likelihood estimation and diagnostics for stable distributions (pp. 379–400). Boston, MA: Birkhäuser Boston.
   Google Scholar
• Rachev, S. (2003). Handbook of heavy tailed distributions in finance: Handbooks in finance. Handbooks in Finance. Amsterdam: Elsevier Science.
   Google Scholar
• Sheppard, M. (2012). Fit all valid parametric probability distributions to data. ALLFITDIST Matlab code (Technical Report). Kennesaw State: Kennesaw State University Department of Mathematics.
   Google Scholar
• Weron, A. & Weron, R. (1995). Computer simulation of Levy alpha-stable variables and processes. Lecture Notes in Physics, 457, 379–392.
   Google Scholar
• Yang, Y. (2012). Option pricing with non-gaussian distribution-numerical approach (Technical Report). New York, NY: Stony Brook University, Department of Applied Mathematics and Statistics.
   Google Scholar
• Yu, J. (2004). Empirical characteristic function estimation and its applications. Econometric Reviews, 23, 93–123.
   Google Scholar
• Zolotarev, V. M. (1964). On the representation of stable laws by integrals. Trudy Matematicheskogo Instituta imeni VA Steklova, 71, 46–50.
   Google Scholar
• Zolotarev, V. M. (1980). Statistical estimates of the parameters of stable laws. Banach Center Publications, 6, 359–376.
   Google Scholar
• Zolotarev, V. (1986). One-dimensional Stable Distributions. Translations of mathematical monographs. Providence, RI: American Mathematical Society.
   Google Scholar