# Skewness in dependent variable (OLS, Gauss Markov, non-normality)

Consider the time series to be estimated with OLS:

$Y_t = a + \bf{X}_t\bf{b} + e_t$

where $Y_t$ is skewed, $\bf{X}_t$ is a vector of regressor values at time $t$, $\bf{b}$ is a vector of coefficient estimates.

Scenario (1): The design matrix is such that the skewness in the response is perfectly accounted for by the design matrix - i.e., there is no non-normality in the residuals. Are our coefficient estimates minimum variance?

Scenario (2): The design matrix is such that the skewness in the response flows into the residuals (suppose for this scenario that the dependent has major skew and the residuals has smaller skew but still comes up on a hypothesis test of non-normality over the estimates of the residuals). Are our coefficient estimates minimum variance? What estimator should I use (I only know of 1: a variant of the Wild bootstrap that accounts for skew)?

A side note. Skewness is a property of single distribution. In time series the sample is a draw from stochastic process. Unless you are working with strictly stationary variables each $Y_t$ might have different distribution.
• @mpiktas If the residuals have mean 0, homoscedasticity and uncorrelated but are skewed $\textbf{and are minimum variance}$, then why does my bootstrap book advertise a benefit of one of the variants of the Wild is that it "accounts for skewness"?