<p>That is illegal because an I(1) series wanders ( doesn't have a constant mean )  and an I(0) series doesn't so they can't be set equal. In order to obtain a valid time series regression, the order on the LHS has to be the same as the order on the RHS. </p>

<p>Note that if both sides are I(1), then a time series regression is okay but only if what is on the RHS is cointegrated with what is on the left. If they aren't cointegrated and both are I(1), then that's what is called a spurious regression. ( i.e: a non-sensical regression ).</p>

CC BY-SA 4.0
2019-05-04T12:16:12.000Z
I think you meant to write "can*not* be set equal".
Giskard
CC BY-SA 4.0
2019-05-04T02:32:24.927Z
2019-05-04T12:37:36.217Z
2019-05-04T12:37:36.217Z
mark leeds
<p>If <span class="math-container">$\{ X_t \}$</span> is a <span class="math-container">$I(1)$</span> series and <span class="math-container">$\{ Y_t \}$</span> is a <span class="math-container">$I(0)$</span> series, would it cause "spurious regression" when regressing like <span class="math-container">$Y_i=\beta_0+\beta_1 X_i+u_i$</span>? Thanks!</p>

CC BY-SA 4.0
2019-05-03T23:37:19.050Z
The subscripts are inconsistent in the regression equation.
Herr K.
<econometrics><co-integration>
Spurious regressions
cxxu96
# Spurious regressions

(Asked by: username_0 on 2019-05-03)

If $\{ X\_t \}$ is a $I(1)$ series and $\{ Y\_t \}$ is a $I(0)$ series, would it cause "spurious regression" when regressing like $Y\_i=\beta\_0+\beta\_1 X\_i+u\_i$? Thanks!

**Tags:** econometrics, co-integration

> **Comments:**
> **username_1**: The subscripts are inconsistent in the regression equation.  

---

## 1 answers

### Answer by username_2 on 2019-05-04. Score: 2

That is illegal because an I(1) series wanders ( doesn't have a constant mean ) and an I(0) series doesn't so they can't be set equal. In order to obtain a valid time series regression, the order on the LHS has to be the same as the order on the RHS.

Note that if both sides are I(1), then a time series regression is okay but only if what is on the RHS is cointegrated with what is on the left. If they aren't cointegrated and both are I(1), then that's what is called a spurious regression. ( i.e: a non-sensical regression ).

> **Comments:**
> **username_3**: I think you meant to write "can*not* be set equal".  

---

