OLS with Time Series Data - yay or nay? I want to model the relationship between two (time-series) variables by using a Vector Autoregressive model (VAR). Since I am not entirely familiar with time series analysis yet, the following question came up in my mind: Is it a good idea to simply model the relationship of the variables by using OLS? I thought it might be a good starting point when writing a text in which I analyze relationships of certain variables, before diving into the more serious analysis. Do you guys think it is a good idea? Or is it rather a no-go (I am asking this since I once heared that OLS is not sophisticated enough for time series analysis)? Do I have to carefully consider something before applying OLS? Thanks in advance!
 A: There are time series models (such as VAR, ARIMA, etc.) and there are estimation techniques (such as OLS, maximum likelihood (ML), etc.). Different models can be estimated by different techniques (sometimes more than one). E.g. a VAR can be estimated by OLS or ML while ARIMA (with a nonempty MA part) cannot be estimated by OLS but can be estimated by ML.
When modelling some data, you need to choose a sensible model and then estimate it. The choice of a sensible model may be hard, I would say, much harder than the estimation of the chosen model. But once the choice is done, you proceed to estimation. If you choose a VAR, then you can estimate it by OLS. Indeed, as Matthew Gunn says, Estimating VAR models with ordinary least squares is a commonplace, perfectly acceptable practice in finance and economics. And as Christoph Hanck correctly adds, if typical VAR assumptions are met (i.e., each equation has the same regressors, the errors are mean independent of the lagged variables - i.e., you got the dynamics right), OLS is even the efficient systems estimator.
Thus the statement OLS is not sophisticated enough for time series analysis is simply not true in general.
