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?


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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