Re: significance of skewness
- From: beliavsky@xxxxxxx
- Date: 1 Jun 2005 05:57:00 -0700
David Duffy wrote:
> > I have a dataset with size N=220. The distribution of this data seems
> > skewed. The true underlying distribution of this data is unknown to me.
> > I want to determine whether the skewness of the data is significant.
> > How can I proceed (in splus)
>
> There is a literature on "robust tests of symmetry".
>
> Resek RW (1974): Alternative tests of skewness: Efficiency
> comparisons under realistic alternative hypothesis. Proc Bus Econ
> Statist Section Am Statist Assoc 1974: 546-551.
>
> There is a bit on graphical tests as well, eg Doksum et al Biometrika 1977
> 64: 473-487
A recent paper on skewness, applied to stock market returns, is "On
More Robust Estimation of Skewness and Kurtosis: Simulation and
Application to the S&P500 Index", by Tae-Hwan Kim and Halbert White,
available in PDF format from
http://ideas.repec.org/p/cdl/ucsdec/2003-12.html . The paper surveys
robust measures of skewness and kurtosis.
Abstract
For both the academic and the financial communities it is a familiar
stylized fact that stock market returns have negative skewness and
excess kurtosis. This stylized fact has been supported by a vast
collection of empirical studies. Given that the conventional measures
of skewness and kurtosis are computed as an average and that averages
are not robust, we ask, "How useful are the measures of skewness and
kurtosis used in previous empirical studies?" To answer this question
we provide a survey of robust measures of skewness and kurtosis from
the statistics literature and carry out extensive Monte Carlo
simulations that compare the conventional measures with the robust
measures of our survey. An application of the robust measures to daily
S&P500 index data indicates that the stylized facts might have been
accepted too readily. We suggest that looking beyond the standard
skewness and kurtosis measures can provide deeper insight into market
returns behaviour.
Here is a recent published paper on testing for asymmetry.
Journal of Financial Econometrics 2005 3(2):169-187
A Test for Symmetry with Leptokurtic Financial Data
Gamini Premaratne
National University of Singapore
Anil Bera
University of Illinois at Urbana-Champaign
Most of the tests for symmetry are developed under the (implicit or
explicit) null hypothesis of normal distribution. As is well known,
many financial data exhibit fat tails, and therefore commonly used
tests for symmetry (such as the standard test based on sample
skewness) are not valid for testing the symmetry of leptokurtic
financial data. In particular, the test uses third moment, which may
not be robust in presence of gross outliers. In this article we propose
a simple test for symmetry based on the Pearson type IV family of
distributions, which take account of leptokurtosis explicitly. Our test
is based on a function that is bounded over the real line, and we
expect it to be more well behaved than the test based on sample
skewness (third moment). Results from our Monte Carlo study reveal that
the suggested test performs very well in finite samples both in terms
of size and power. Simulation results also support our conjecture of
the tests to be well behaved and robust to excess kurtosis. We apply
the test to some selected individual stock return data to illustrate
its usefulness.
KEYWORDS: test, kurtosis, Monte Carlo study, Pearson family of
distributions, Rao's score test, skewness, tan-1(·) function
.
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