Contents
Is normality important for OLS?
The condition of normality of the residuals is useful when residuals are also homoskedastic. The result is then that OLS has the smallest variance between all of the estimator (linear OR non-linear).
What happens when Homoscedasticity is violated?
Heteroscedasticity (the violation of homoscedasticity) is present when the size of the error term differs across values of an independent variable. The impact of violating the assumption of homoscedasticity is a matter of degree, increasing as heteroscedasticity increases.
How do you determine normality of error?
Normality is the assumption that the underlying residuals are normally distributed, or approximately so. While a residual plot, or normal plot of the residuals can identify non-normality, you can formally test the hypothesis using the Shapiro-Wilk or similar test.
Which is more serious, failure of OLS or non-normality?
This probable failure of OLS assumptions is far more serious than the failure of normality . The assumption that the disturbances are normal allows exact inference about the estimates and standard errors of the estimated coefficients.
What are the consequences of non normality for time series data?
By standardized res, I mean your non-normal residuals divided by SEE of your estimated equation. ith observation implies to select the (in absolute value) largest std residuals. Can you help by adding an answer? What to do if the residuals in NR are not normally distributed ?
Which is the minimum length of the OLS procedure?
The OLS procedure is nothing more than nding the orthogonal projection of y on the subspace spanned by the regressors, because then the vector of residuals is orthogonal to the subspace and has the minimum length. This interpretation is very important and intuitive.
What happens when the normality assumption is not valid?
When the normality assumption is not valid (and the other assumptions are) the estimates are still consistent and the central limit theorem allows one to make inferences that are valid in an asymptotic sense. Wooldridge, Introductory Econometrics, (Chapter 5 in 4th edition) contains a good introduction to this asymptotic theory.