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I have just started learning about time series analysis. I had a doubt regarding AR models. I understand that in Auto Regression, we regress one variable on values of the same variable at different past time points. And I know that ,in linear regression the independent variables must be independent of each other. But wouldn't the values of the same variable in a AR model be dependent on each other and cause multicollinearity? And if there is multicollinearity how do we deal with it? Please explain if I am correct in my understanding or am missing something. Thanks in advance...

joy
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    "And I know that, in linear regression the independent variables must be independent of each other" -- no, this is not true. Multicollinearity and dependence are different concepts. – Adrian Oct 23 '15 at 15:00
  • @ adrian can you please elaborate? am i incorrect in understanding that multicollinearity happens in linear regression when there is linear dependence (ie. correlation) between independent variables? Tnx.. – joy Oct 23 '15 at 15:05
  • Have a look at https://stats.stackexchange.com/questions/137425/how-seriously-should-i-consider-the-effects-of-multicollinearity-in-my-regressio/137433#137433 – Adrian Oct 23 '15 at 15:13
  • Consider the model y ~ x1 + x2. If x1 and x2 are perfectly correlated, you're in trouble. But a correlation that is neither 1 nor -1 is not an issue (unless it's extremely close to either of those numbers). – Adrian Oct 23 '15 at 15:14
  • @adrian thnx for the link.. now if i apply this to my original question, i think it is highly probable that the independent variables in a AR model will have a high correlation between themselves.. how can we deal with multicollinearity in that case? – joy Oct 23 '15 at 17:13
  • Edit your question and tell us the assumptions of your AR model. Usually there's an iid error term. Does it have positive variance? – Adrian Oct 23 '15 at 18:12
  • I think the fact that your model is autoregressive is not particularly important in this case. Just look at posts tagged with `multicollinearity` and see if they happen to answer your question. Dave Giles has a few good posts about multicollinearity in his blog, they are worth reading. – Richard Hardy Oct 23 '15 at 19:59
  • @Richard, Thnx for your reply.. I will definitely go through your leads.. Actually I am not building any model, I just started reading about Auto Regressive models and had the doubt that since here the independent variables are basically the same variable values but at different time points, they must have high correlation between themselves, which can cause multicollinearity.. – joy Oct 24 '15 at 07:10
  • I have exactly the same doubts. Have you come to any conclusions? – Arthur Aug 18 '17 at 21:23

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