I hope I formulated the question correctly, but I am purely interested in heteroskedasticity: cov($e_i$,$e_j$) and not in autocorrelation with the dependent variables.
So positive correlation of the error terms will give you the standard graphs, in which large errors follow up on each other and you get these kind of typical time series where large volatility will stay for a while and periods of low volatility are observed, right?
But what about negative correlation? Then large errors will be quickly followed by small errors and vice versa right? How would that typically look like?
Also small side question, the left graph I would depict as positively correlated in its residuals, but someone told me that the right graph could be a case of negative correlation. But this is incorrect right? To me that seems more like a classic case of autocorrelation.