<p>Yes there is a difference. The right tailed test in Eviews is designed based on:
<em><a href="https://mpra.ub.uni-muenchen.de/58791/1/MPRA_paper_58791.pdf" rel="nofollow noreferrer">Caspi, 2013</a></em>.</p>
<p>If you're looking for just the operational difference between the two tests: The standard ADF test is also one sided with <span class="math-container">$H_0: \phi = 0$</span> against <span class="math-container">$H_1: \phi&lt;0$</span> (so in practical terms the null hypothesis is <span class="math-container">$H_0 \geq 0$</span>). Rejection of null would mean no unit root and the series is stationary.</p>
<p>For the right tailed test the alternative is <span class="math-container">$H_1: \phi &gt;0$</span>. So the rejection of null means that the process has no unit root but is non-stationary (explosive type).</p>
<p>I do want to mention that I do not know theoretical difference as in how would one go about designing such a test because the null distribution is same but the critical values for different alternatives need to different. But how, I don't know.</p>

CC BY-SA 4.0
2022-03-10T10:55:55.807Z
*may still have unit root class of non-stationarity*: How so if the null of a unit root is being rejected?
Richard Hardy
CC BY-SA 4.0
2022-03-10T14:23:51.377Z
@RichardHardy: Yeah I am not fully sure ofy statement myself. By unit root class I mean that explosive series such as say $y_t = 1.2 y_{t-1} + \epsilon_t$ is also unit root *type* non stationarity because it will become stationary after differencing. In this example by first difference.
Dayne
CC BY-SA 4.0
2022-03-10T14:29:56.030Z
I was actually planning of posting a question on CV because I am unable to see how the critical values be decided from df table. After all the null distribution is same. In usual tests, we take one side of the tail...I unable to directly see this here.
Dayne
CC BY-SA 4.0
2022-03-10T15:20:28.563Z
I think this is a poor use of terminology, because the root of the characteristic polynomial is not 1. I suggest rephrasing. Moreover, I would think twice before differencing anything that does not have a unit. Instead of achieving stationarity, the result will be overdifferencing with all of its negative consequences.
Richard Hardy
CC BY-SA 4.0
2022-03-11T08:47:28.467Z
Point noted. Deleting the last part.
Dayne
CC BY-SA 4.0
2022-03-09T05:46:25.130Z
2022-03-11T08:48:59.633Z
2022-03-11T08:48:59.633Z
Dayne
<p>Is there a difference between right-tailed ADF and standard ADF tests in Eviews?</p>

CC BY-SA 4.0
2022-03-08T20:09:55.090Z
To my knowledge, the difference is in the null/alt hypotheses. With the ADF test, we test the null of 'unit root' vs an alternative of 'no unit root'. With the right-tailed ADF, the null is 'unit root' versus an alternative of 'mildly explosive process' (i.e a process integrated of higher order than 1). In other words, you should be using a test like this if you expect your data to be characterised by a fairly explosive process. This is just on an intuitive level, but you should check all the details with Caspi (2017) https://www.jstatsoft.org/article/download/v081c01/1161
EB3112
<econometrics>
Is there a difference between right-tailed ADF and standard ADF test?
Athana
# Is there a difference between right-tailed ADF and standard ADF test?

(Asked by: username_0 on 2022-03-08)

Is there a difference between right-tailed ADF and standard ADF tests in Eviews?

**Tags:** econometrics
> **Comments:**
> **username_1**: To my knowledge, the difference is in the null/alt hypotheses. With the ADF test, we test the null of 'unit root' vs an alternative of 'no unit root'. With the right-tailed ADF, the null is 'unit root' versus an alternative of 'mildly explosive process' (i.e a process integrated of higher order than 1). In other words, you should be using a test like this if you expect your data to be characterised by a fairly explosive process. This is just on an intuitive level, but you should check all the details with Caspi (2017) https://www.jstatsoft.org/article/download/v081c01/1161  

---

## 1 answers

### Answer by username_2 on 2022-03-09. Score: 1

Yes there is a difference. The right tailed test in Eviews is designed based on:
*[Caspi, 2013](https://mpra.ub.uni-muenchen.de/58791/1/MPRA_paper_58791.pdf)*.

If you're looking for just the operational difference between the two tests: The standard ADF test is also one sided with $H\_0: \phi = 0$ against $H\_1: \phi<0$ (so in practical terms the null hypothesis is $H\_0 \geq 0$). Rejection of null would mean no unit root and the series is stationary.

For the right tailed test the alternative is $H\_1: \phi >0$. So the rejection of null means that the process has no unit root but is non-stationary (explosive type).

I do want to mention that I do not know theoretical difference as in how would one go about designing such a test because the null distribution is same but the critical values for different alternatives need to different. But how, I don't know.

> **Comments:**
> **username_3**: *may still have unit root class of non-stationarity*: How so if the null of a unit root is being rejected?  
> **username_2**: @RichardHardy: Yeah I am not fully sure ofy statement myself. By unit root class I mean that explosive series such as say $y_t = 1.2 y_{t-1} + \epsilon_t$ is also unit root *type* non stationarity because it will become stationary after differencing. In this example by first difference.  
> **username_2**: I was actually planning of posting a question on CV because I am unable to see how the critical values be decided from df table. After all the null distribution is same. In usual tests, we take one side of the tail...I unable to directly see this here.  
> **username_3**: I think this is a poor use of terminology, because the root of the characteristic polynomial is not 1. I suggest rephrasing. Moreover, I would think twice before differencing anything that does not have a unit. Instead of achieving stationarity, the result will be overdifferencing with all of its negative consequences.  
> **username_2**: Point noted. Deleting the last part.  

---

