Suppose we are estimating a model of a stocks return (r t ) of the form:

r t =a+br t-1 +e t

where e t is an error term.

If we suspect the variance of e t changes systemically with time (for e.g. with a time trend), what would be the impact on standard OLS estimation and inference? In addition, if we believe the variance of e t influences the return (r t ), how should we specify a GARCH model to account for that?