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What is the difference between these time series AR(1) regression models (lead in the dependent vs lag in the dependent variable)?

$$\begin{align}y_t = constant + \alpha y_{t-1} + error \tag{1}\label{eq1}\\ y_{t+1} = constant + \alpha y_{t} + error \tag{2}\label{eq2}\end{align}$$

Will they have different coefficients?

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  • $\begingroup$ Consider posting questions like this on Cross Validated instead. There is a higher concentration of questions of this type and probably more experts to answer them. $\endgroup$
    – Richard Hardy
    Dec 5, 2022 at 9:46

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There is no difference. Coefficients for both AR models will be exactly the same.

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There will be no difference between these two models. You've just indexed the variable $y$ in a different style.

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