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...

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    $\begingroup$ "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. $\endgroup$ – Adrian Oct 23 '15 at 15:00
  • $\begingroup$ @ 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.. $\endgroup$ – joy Oct 23 '15 at 15:05
  • $\begingroup$ Have a look at stats.stackexchange.com/questions/137425/… $\endgroup$ – Adrian Oct 23 '15 at 15:13
  • $\begingroup$ 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). $\endgroup$ – Adrian Oct 23 '15 at 15:14
  • $\begingroup$ @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? $\endgroup$ – joy Oct 23 '15 at 17:13

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