Question

Attached are the results of a diagnostic test on an estimated model, autocorrelation, heteoskedasticity and non-normality respectivey, can you please comment on the results and state the conclusion for each test using a 5% significance level

Breusch-Godfrey Serial Correlation LM Test F-statistic Obs R-squared 0.7659 0.7612 0.458959 Prob. F(4,438) 1.861565 Prob. Chi-Square(4) Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/19 Time: 22:02 Sample: 1982M01 2019M02 Included observations: 446 Presample missing value lagged residuals set to zero. Coefficient Std. Error t-Statistic Prob. Variable 0.005680 0.625767 0.009077 0.9928 0.018168 0.148177-0.122612 0.9025 0.016018 0.229732 0.069726 0.9444 0.000919 0.215035 0.004275 0.9966 0.003859 0.048327 0.079862 0.9364 0.045255 0.048153 0.939827 0.3478 0.033979 0.048087 0.706610 0.4802 0.029215 0.048412 0.603475 0.5465 MKT RF HML SMB RESID(-1) RESID(-2) RESID(-3) RESID(-4) Mean dependent var5.03E-16 12.86278 7.976000 8.049548 8.004998 1.999604 R-squared Adjusted R-squared -0.011741 S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic 0.004174 12.93807 73318.41 Akaike info criterion Schwarz criterion 1770.648 Hannan-Quinn criter 0.262262 Durbin-Watson stat Prob(F-statistic) 0.968044 View Proc Object Print Name Freeze Estimate Forecast Stats Resids F-statistic Obs R-squared Scaled explained SS 1.714967 Prob. F(3,442) 5.131728 Prob. Chi-Square(3) 76.36389 Prob. Chi-Square(3) 0.1632 0.1624 0.0000 Test Equation: Dependent Variable: RESIDA2 Method: Least Squares Date: 05/22/19 Time: 21:51 Sample: 1982M01 2019M02 Included observations: 446 Variable Coefficient Std. Error t-Statistic Prob. 125.6237 51.28761 2.449397 0.0147 -0.135755 1.124011 0.120777 0.9039 6.140549 2.745221 2.236815 0.0258 1.013191 1606211 -0.630796 0.5285 MKT_RFA2 HMLA2 SMBA2 R-squared n Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic 165.0801 909.7497 16.46834 0.011506 Mean dependent var S.D. dependent var Akaike info criterion 0.004797 907.5651 16.50511 16.48284 2.084658 3.64E+08 Schwarz criterion -3668.439 Hannan-Quinn criter 1.714967 Durbin-Watson stat 0.163151 Prob(F-statistic) Path clusers 451587461documents DB none View Proc Object Print Name Freeze Estimate Forecast Stats Resids 240 T Series: Residuals Sample 1982M01 2019M02 Observations 446 200- -5.03e-16 0.711687 160- Mean Median Maximum 76.96999 Minimum 125.4659 Std. Dev. 12.86278 Skewness 2.962990 Kurtosis 31.30258 120 80 40- Jarque-Bera 15538.51 Probability 0.000000 -120 100 80 -60 40 -20 0 20 40 6080

Answer 1

for autocorrelation test (Breusch-Godfrey Serial Correlation LM Test)
p-value = 0.7659

p-value > alpha (0.05)
hence
we fail to reject the null hypothesis

there is not evidence of correlation

2)
for homeskedasticity
p-value = 0.1632

p-value > 0.05
hence we fail to reject the null hypothesis
we conclude that there is no evidence of heteroskedasticity

3)
Normality test
p-value = 0.0000 < alpha
hence we reject the null hypothesis

we conclude that data does not follow normal distribution