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Shaikh A. Hamid, Tej S. Dhakar: Anamolous Behavior of the Volatility of Nasdaq
Composite Index: 1971 To 2017

skewness S and kurtosis K under the normality condition, the Jarque-Bera statistic
n  (K  )3 2 
 S 2   follows a Chi-square distribution with 2 degrees of freedom.


6  4 
Many studies have used the dummy variable methodology to detect market
seasonality. Chien, Lee and Wang (2002) provide statistical analysis and empirical
evidence that the methodology may provide misleading results. We avoid this
methodology.

We test the following hypotheses:

1. If the variability of the daily absolute percentage changes for a given month is
significantly different from the remaining eleven months. The hypothesis test for a
given month i is: Ho: µi = µj vs. Ho: µi  µj where j = {1, 2, …, i-1, i+1, ,,,, , 11,
12}. µi is the mean of MAPC values for month i.

2. If the means of the monthly absolute percent changes for a given month is different
from the means of the monthly absolute percent changes for the other eleven
months. The hypothesis test for a given month i is: Ho: i = j vs. Ho: i  j, where
j = {1, 2, …, i-1, i+1, …, 11, 12}.

Since we found the variances for the periods i and j to be unequal in many cases, we
decided to use the more conservative t-test assuming unequal variances.

III. THE DATA AND DESCRIPTIVE STATISTICS

The data consists of 11,817 values of daily percentage changes and 562 values of
mean of absolute daily percentages changes for a month from March 1971 to
December 2017. The data for the February 1971 was not included in the sample as it
was a partial month, Nasdaq having originated on February 5, 1971.

Over this period, the value of NASDAQ Composite Index increased from 101.34 at
the end of February 1971 to 6903.39 at the end of December 2017, 6713% – with an
average percentage increase of 0.956% per month or 11.47% increase per year. The
mean of absolute percent changes during a month (MAPC) averaged 0.81% over this
period. The MAPC in the NASDAQ Composite Index for the total period is highly
significant (p = 0.00). The standard deviation of MAPC during this period was 0.56%.

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