For Barrick Gold, the JarqueBera test statistic of 18.73 exceeds the
critical values for any reasonable significance level to lead to the
conclusion that the daily returns do not follow a normal distribution.
Since the excess kurtosis statistic is greater than zero, the appearance
is that the daily returns follow a distribution that features
leptokurtosis.
Researchers have suggested that the leptokurtosis
arises from a pattern of volatility in financial markets where periods
of high volatility are followed by periods of relative stability.
A pvalue for the test statistic is calculated as a chisquare
distribution probability and, with Microsoft Excel, is computed with
the function:
CHIDIST(test_statistic, 2)
↑
degrees of freedom
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View Full DocumentEcon 325 – Normality Test
9
For the Bank of New York, the calculation of a pvalue for the Jarque
Bera test statistic is illustrated in the graph below.
A statistical result is that the chisquare distribution with two degrees
of freedom is an exponential distribution.
PDF for the
2
χ
distribution
with 2 degrees of freedom
2.31
0
area = pvalue = 0.315
↑
JarqueBera test statistic
for Bank of New York
It is clear that the calculated pvalue is greater than any standard
significance level
α
to suggest that there is no evidence to reject the
null hypothesis of a normal distribution for the daily returns of the
Bank of New York.
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 Fall '10
 WHISTLER
 Normal Distribution, Variance, Kurtosis, excess kurtosis, normality test

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