<p>There is no difference. Coefficients for both AR models will be exactly the same.</p>

CC BY-SA 4.0
2022-12-04T21:35:08.353Z
2022-12-04T21:35:08.353Z
csilvia
<p>There will be no difference between these two models. You've just indexed the variable <span class="math-container">$y$</span> in a different style.</p>

CC BY-SA 4.0
2022-12-04T21:55:10.357Z
2022-12-05T10:38:53.183Z
2022-12-05T10:38:53.183Z
hmmmm
<p>What is the difference between these time series AR(1) regression models (lead in the dependent vs lag in the dependent variable)?</p>
<p><span class="math-container">$$\begin{align}y_t = constant + \alpha y_{t-1} + error \tag{1}\label{eq1}\\
y_{t+1} = constant + \alpha y_{t} + error \tag{2}\label{eq2}\end{align}$$</span></p>
<p>Will they have different coefficients?</p>

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2022-12-05T09:46:00.937Z
Consider posting questions like this on [Cross Validated](https://stats.stackexchange.com/questions) instead. There is a higher concentration of questions of this type and probably more experts to answer them.
Richard Hardy
<regression><time-series>
Comparison of two AR(1) regression models (lead in dependent vs lag in dependent variable)
Shushue
# Comparison of two AR(1) regression models (lead in dependent vs lag in dependent variable)

(Asked by: username_0 on 2022-12-04)

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?

**Tags:** regression, time-series
> **Comments:**
> **username_1**: Consider posting questions like this on [Cross Validated](https://stats.stackexchange.com/questions) instead. There is a higher concentration of questions of this type and probably more experts to answer them.  

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## 2 answers

### Answer by username_2 on 2022-12-04. Score: 2

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


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### Answer by username_3 on 2022-12-04. Score: 2

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


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