# Should we test error terms for auto correlation or multicollinearity

I understand the basic difference in definition between multicollinearity and autocorrelation. I.e multicollinearity describes a linear relationship between whereas autocorrelation describes correlation of a variable with itself given a time lag.

When should I test for these as part of hypotheses testing? When fitting a model to a time series are the error terms tested for autocorrelation or multicollinearity? Why one over the other?

In a linear regression between Y and X with no time component, I suppose the answer is easy? We fit a linear model and test the residuals for multicollinearity and not autocorrelation because we are not considering time as a factor here. I am sorry for such a naive question.

• There was a question with almost exactly the same title. Did you search SE? – Aksakal Jan 5 '15 at 18:51
• How does one "test residuals for multicollinearity"? What specifically do you mean by "multicollinearity" of a set of residuals (which is just a collection of numbers)? – whuber Jan 5 '15 at 19:21
• It's an interesting question: when do residuals become collinear? When two variables are impacted by exactly the same shock. For instance, $y_t=t+\varepsilon$ and $z_t=t^2+\varepsilon$, teh same errors. – Aksakal Jan 5 '15 at 19:54
• @Aksakal: Collinearity is a relationship among vectors, not a property of a set of numbers. So what specifically do you mean by "residuals become collinear"? Collinear with what? – whuber Jan 5 '15 at 21:35
• @Victor, if it's univariate series, then mutlicollinearity is not even applicable here to residuals. It's for vectors, particularly, explanatory variable vectors. – Aksakal Jan 5 '15 at 22:01