I am trying to perform an OLS on time series for a project for college. The professor told me that I need my regressors to be normal in order to justify the use of a linear regression. His argument was that only if the joint distribution of dependent and independent variables were normal (and thus every marginal distribution were normal too) the expected values of the dependent conditioning for the values of our regressors would line up on a line, estimated by the OLS. Though I found an entirely different opinion on a reliable forum. This opinion stated that normality of the regressors does not matter. It doesn't cause any problem in the use of OLS. Can anyone confirm one or the other view? Can you please give me a link to a paper I could make reference ?
In regression we condition on X so its distribution is irrelevant. Only the conditional distribution of Y (or equivalently, the residuals) is relevant. Although there may be special considerations in time series (e.g., how are you handling autocorrelation?) your professor is incorrect.