SSE = 100 DW statistic = 141 Squared residuals regression Intercept Coeffecient = 3 Intercept Se = 0.577 Lagged Residual squared Coeffecient = 0.28 Lagged Residual squared Se = 0.185 Does the ARCH model exhibit conditional hetroskedasticity? and are the standard errors (Se) in your AR model unreliable?
I would like to learn the answer to this question as well.
Was the number of observations given? if so I think we could do BP test for conditional heteroskedasticity, and if it is present then the se’s are too small, resulting in t-stats too large and increased type 1 errors.
BP test with a Chi-Squared table will do the trick. REFER: http://www.analystforum.com/phorums/read.php?12,685427,686726#msg-686726 We need to check if the residuals error terms are having constant variance (i.e. test for homoskedasticity). So we use Breusch-Pagan-test to check for conditional heteroskedasticity by taking the [(no-of-observation)*( coefficient of determination)] as the t(stat-calculated) and check it against the Chi-Squared table value where DoF = no of independent variable. It’s only when we reject the null (of Conditional heteroskedasticity) we are safe to assume the model is good for use. It we fail to reject the null, then we conclude all our inferences were inappropriate due to the standard errors/ test statistcs being wrongly estimated and probably of Type-I error increases. Then on, we try to compute the Robust standard errors or go for the Generalized leased squares and assume that the derived regression equation, no longer has the heteroskedasticity issue.
N = 60 K = 1
lagged residual is less than 1, therefore the variance will vary from time to time (non constant variance) hence the error term exhibit heteroskedasticity. if the lagged residual is 0, the error term is constant over time. we need to test the significant of lagged residual, if the lag residual is sinificant then its an ARCH. Whats the P value? is it given?
so the BP stat would be 60x0.185 = 11.1 where critical value is 3.841 therefore reject the null hypothesis of no conditional heteroskedasticity and the standard errors are unreliable. Can someone confirm this? or skumar can you let me know if this is what was done in the solution? I’m pretty sure the R^2 is that of the residuals and not of the coefficients.