American Journal of Theoretical and Applied Statistics
Volume 2, Issue 2, March 2013, Pages: 38-41
Received: Mar. 6, 2013;
Published: Apr. 2, 2013
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E. Reschenhofer, Department of Statistics and Operations Research, University of Vienna, Vienna, Austria
Comparing the order statistics of daily returns of the S&P 500 index from 03.01.1950 to 04.03.2013 with the corresponding rankits, a linear scale dilation is observed. This observation is used to derive a five-parameter density function for the parsimonious description of the unconditional distribution of stock returns. The typical graph of this density function looks like a wizard's hat. Its signature feature is the discontinuity at zero.
Linear Scale Dilation of Asset Returns, American Journal of Theoretical and Applied Statistics.
Vol. 2, No. 2,
2013, pp. 38-41.
A. Azzalini, A class of distributions which includes the normal ones, Scandinavian Journal of Statistics 12, pp. 171-178, 1985.
A. Azzalini, Further results on a class of distributions which includes the normal ones, Statistica 46, pp. 199-208, 1986.
A. Azzalini, The skew-normal distribution and related multivariate families, Scandinavian Journal of Statistics 32, pp. 159-188, 2005.
F. M. Aparicio and J. Estrada, Empirical distributions of stock returns: European securities markets, 1990-95, The European Journal of Finance 7, pp. 1-21, 2001.
T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31, pp. 307-327, 1986.
R. F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50, pp. 987-1007, 1982.
E. F. Fama, The behavior of stock market prices, Journal of Business 38, pp. 34-105, 1965.
C. Fernandez and M. F. Steel, On Bayesian modeling of fat tails and skewness, Journal of the American Statistical Association 93, pp. 359–371, 1998.
S. J. Kon, Models of stock returns - a comparison, The Journal of Finance 39, pp. 147-165, 1984.
F. M. Longin, The choice of the distribution of asset returns: how extreme value theory can help?, Journal of Banking and Finance 29, pp. 1017–1035, 2005.
B. Mandelbrot, The variation of certain speculative prices, Journal of Business 34, pp. 392-417, 1963.
S. Nadarajah, A generalized normal distribution, Journal of Applied Statistics 32, pp. 685–694, 2005.
R. R. Officer, The distribution of stock returns, Journal of the American Statistical Association 67, pp. 807-812, 1972.
H. T. Robertson and D. B. Allison, A novel generalized normal distribution for human longevity and other negatively skewed data, PLoS ONE 7, e37025, 2012.
J. P. Royston, Expected normal order statistics (exact and approximate), Journal of the Royal Statistical Society Series C (Applied Statistics) 31, pp. 161-165, 1982.