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From looking at textbooks, I see that the equation used for estimating auto-regression is different from the equation used to estimate multiple-regression.

But, if I used successive values from a time series with multiple regression, instead of using auto-regression, would I get exactly the same results?

I ask because I would like to use auto-regression on a time series to predict, but I would also like to include other independent variables as well. Should I just use multiple-regression, or is there some better way to do it?

Edit/update: Thanks for the 1 answer so far. Is there any way I can trick or force multiple regression to give the same results as auto-regression, for example by using the differences between successive values in the time series, by using ratios of successive values, or by using logs of all the values, etc?

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They are definitely not the same. Autocorrelation inflates type-I error (Scheffé, 1959), such that with a nominal $\alpha$ type-I error rate with of 0.05 with autocorrelation of $\rho=0.4$, the true $\alpha$ approaches 0.2 (Raadt, in-press). If you want to include other predictors in your model, a first step might be either a hierarchical linear model with an AR(1) correlation structure for level-1 error or perhaps an ARIMAX model.

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