Econometric

Testing for normality: MANUF

H0: errors are normally distributed (z=0 & K=3)

H1: errors are not normally distributed (z≠0 & K≠3)

Decision rule:

Reject the null hypothesis if the histogram is not bell shaped (either leptokurtic distribution or a platykurtic distribution) and using 5% significance level, if the JB statistic is greater than the critical chi-squared value or p-value given on the output is less than 0.05.

Test statistic:

By observation, the errors look to have a leptokurtic distribution consisting of fatter tails and with a higher peak at the mean.

The JB statistic = 46939482 > 5.99 (given α= 0.05, with df = ?)

P-value = 0.00000 < 0.05

Conclusion:

Testing for misspecification: MANUF

H0: correct functional form

H1: incorrect functional form

Decision Rule:

If p-value of the Likelihood ratio is less than 0.05 we reject the null hypothesis.

Ramsey RESET Test

Equation: UNTITLED

Specification: MANUF-RF C MKT_RF SMB HML MOMENTUM

Omitted Variables: Squares of fitted values

Value df Probability

t-statistic 0.481280 1014 0.6304

F-statistic 0.231630 (1, 1014) 0.6304

Likelihood ratio 0.232974 1 0.6293

F-test summary:

Sum of Sq. df Mean Squares

Test SSR 0.458087 1 0.458087

Restricted SSR 2005.809 1015 1.976166

Unrestricted SSR 2005.351 1014 1.977663

Unrestricted SSR 2005.351 1014 1.977663

LR test summary:

Value df

Restricted LogL -1792.202 1015

Unrestricted LogL -1792.086 1014

Unrestricted Test Equation:

Dependent Variable: MANUF-RF

Method: Least Squares

Date: 10/27/12 Time: 16:12

Sample: 1927M01 2011M12

Included observations: 1020

Variable Coefficient Std. Error t-Statistic Prob.

C -0.011863 0.048190 -0.246171 0.8056

MKT_RF 0.991203 0.009015 109.9489 0.0000

SMB -0.093817 0.014074 -6.666092 0.0000

HML 0.178105 0.013816 12.89077 0.0000

MOMENTUM 0.045642 0.010732...