## Chi -Square !

Could you help me solve this question. Many thanks !

The Dow-Jones daily returns for the period 1920-2006 under the normal likelihood show a
raw mean of 0.00020 and standard deviation of 0.01140. Skewness is -0.6673 and kurtosis
29.7454.
(a) Calculate the annual mean and variance.
(b) Calculate the Jarque-Bera statistic and perform the hypothesis test. Write down the
null and alternative hypotheses. Run a  2 test with 2 degrees of freedom. Refer to the
tables given for the chi-square distribution. (N = 19566)
(c) What does the term “normally distributed returns” mean? What do your results say
)
4
( ( 3)
6
3
2 
JB  N S  K
Tail (right)  2 Tail (right)  2
0.5 1.38629
0.95 0.10259 0.25 2.77259
0.99 0.0201 0.1 4.60517
0.975 0.05064 0.05 5.99146
0.95 0.10259 0.025 7.37776
0.9 0.21072 0.01 9.21034
0.75 0.57536 0.005 10.5966