A generalized skewness statistic for stationary ergodic martingale differences

被引：0

作者：

Kaehler B.D. ^{[1
]}

Maller R.A. ^{[1
]}

机构：

[1] School Finance and Appl. Statist., and Math. Sci. Inst., Australian National Univ., Canberra

来源：

Mathematical Methods of Statistics | 2010年 / 19卷 / 3期

基金：

澳大利亚研究理事会;

关键词：

asymmetry; central limit theorem; ergodic; martingale; skewness; stationary;

D O I：

10.3103/S106653071003004X

中图分类号：

学科分类号：

摘要：

We present a class of generalized skewness statistics depending on a parameter β < 0 and containing the usual skewness statistic when β = 3, but providing greater flexibility for modelling and testing skewness when β ≠ 3. The statistics' suitability for financial applications is illustrated using a large data set from the Australian share market. Data is assumed to be observations on stationary ergodicmartingale differences with possibly leptokurtic marginals, rather than independent identically distributed samples. The statistics can be studentized for use in hypothesis testing. Proof is provided of their asymptotic distributions undermild assumptions. Rates of convergence and power of the tests against skewed alternatives are assessed using simulation. © 2010 Allerton Press, Inc.

引用

页码：267 / 282

页数：15

共 21 条

[1]

Bai J., Ng S., Tests for Skewness, Kurtosis, and Normality for Time Series Data, J. Bus. Econom. Statist., 23, 1, pp. 49-60, (2005)

[2]

Bingham N.H., Kiesel R., Schmidt R., A Semi-Parametric Approach to Risk Management, Quant. Finance, 3, 6, pp. 426-441, (2003)

[3]

Danielsson J., de Vries C.G., Tail Index and Quantile Estimation with Very High Frequency Data, J. Empirical Finance, 4, pp. 241-257, (1997)

[4]

Danielsson J., de Vries C.G., Value-at-Risk and Extreme Returns, (1998)

[5]

Heyde C.C., A Risky Asset Model with Strong Dependence through Fractal Activity Time, J. Appl. Probab., 36, pp. 1234-1239, (1999)

[6]

Heyde C.C., Hall P., Martingale Limit Theory and Its Application, (1980)

[7]

Hull J.C., Options, Futures and Other Derivatives, (2003)

[8]

Hurst S.R., Platen E., The Marginal Distribution of Returns and Volatility, -Statistical Procedures and Related Topics, pp. 301-314, (1997)

[9]

Hurst S.R., Platen E., Rachev S.T., Subordinated Market Index Models: A Comparison, Finan. Eng. Japanese Markets, 4, pp. 97-124, (1997)

[10]

Jansen D.W., de Vries C.G., On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective, Rev.Econom. Statist., 73, 1, pp. 18-24, (1991)

← 1 2 3 →