I'm trying to understand the issues with using OLS regression when our data exhibits autocorrelation. Let's say you simulate a process where:
t = [1, 2, 3, ..., 100] e = 100 random normal variables from N(0, 5) y = 2 * t + e
Because of this set up, there is obvious autocorrelation of y. You nevertheless build a basic OLS model where y is the response and t is the predictor.
What are the issues autocorrelation like this causes? In many of the regression books, we talk about issues if variance is non-constant or distribution of Y | t is non-normal. If I recall correctly, such model violations affect the standard errors of our estimates and thus make it tougher to estimate true parameters.
But I don't recall any discussion on what happens when autocorrelation is present. Yet anywhere I look, it just says autocorrelatoin or non independence is bad. What exactly is the issue that prevents us from using OLS to model the process described above - and thus necessitates a time series technique.