norTestPRN

73 exceeds the critical values for any reasonable

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For Barrick Gold, the Jarque-Bera 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 p-value for the test statistic is calculated as a chi-square distribution probability and, with Microsoft Excel, is computed with the function: CHIDIST(test_statistic, 2) degrees of freedom
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Econ 325 – Normality Test 9 For the Bank of New York, the calculation of a p-value for the Jarque- Bera test statistic is illustrated in the graph below. A statistical result is that the chi-square 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 = p-value = 0.315 Jarque-Bera test statistic for Bank of New York It is clear that the calculated p-value 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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