Null hypothesis on intercept in unit root test

For technical questions regarding estimation of single equations, systems, VARs, Factor analysis and State Space Models in EViews. General econometric questions and advice should go in the Econometric Discussions forum.

Moderators: EViews Gareth, EViews Moderator

karsten_kohler
Posts: 4
Joined: Tue Mar 28, 2017 3:54 am

Null hypothesis on intercept in unit root test

Postby karsten_kohler » Sat Sep 23, 2017 9:37 am

Hello there!

I would like to know what the null hypothesis on the intercept in an Augmented Dickey Fuller (ADF) unit root test in EViews is. When running an ADF test in EViews, there are three options

a) no intercept and no trend
b) intercept
c) intercept and trend.

If I'm not mistaken, Hamilton (1994, Time Series Analysis, chap. 17), however, distinguishes four cases:

1) y(t) = p.y(t-1) + e(t)
HO: p = 1
HA: |p| < 1

2) y(t) = a + p.y(t-1) + e(t)
HO: p = 1, a = 0
HA: |p| < 1, a ≠ 0

3) y(t) = a + p.y(t-1) + e(t)
HO: p = 1, a ≠ 0
HA: |p| < 1, a = 0

4) y(t) = a + p.y(t-1) + d.t + e(t)
HO: p = 1, d = 0
HA: p < 1,d ≠ 0

It is thus not clear to me, what the null hypothesis on the intercept (a in my notation) is when I select option b) in EViews. Does it correspond to Hamilton's case 2) a=0, or 3) a ≠ 0 ?

I couldn't find the answer in the Eviews Guide. Any help is highly appreciated.

KrilleJ
Posts: 38
Joined: Fri Feb 20, 2015 6:15 am

Re: Null hypothesis on intercept in unit root test

Postby KrilleJ » Wed Sep 27, 2017 5:39 am

when perorming the ADF tests.In the EViews test procedures there are no restrictions placed on the deterministic components of the test regression.

Under a) a pure AR model (without deterministic trend components) is specified: y_t=\rho*y_{t-1}+\eps_t. The test performed is on \rho. Under b) and c), deterministic components are added to the test regression (only intercept or intercept and time trend), but the test is still on \rho. Hence, the null hypothesis involves only \rho. You can of course construct joint tests on \rho and the deterministic components (by setting up an Equation object), but the critical values will not be the (A)DF critical values.

karsten_kohler
Posts: 4
Joined: Tue Mar 28, 2017 3:54 am

Re: Null hypothesis on intercept in unit root test

Postby karsten_kohler » Wed Sep 27, 2017 6:14 am

Thank you for your answer.

The problem is that according to Hamilton, the distribution of the test statistic for H0: p = 1 depends on the assumption made about the intercept.

KrilleJ
Posts: 38
Joined: Fri Feb 20, 2015 6:15 am

Re: Null hypothesis on intercept in unit root test

Postby KrilleJ » Thu Sep 28, 2017 4:17 am

That is absolutely true. The critical values depends both on what deterministic components you include and whether you test a simple or joint hypothesis. Tabulations exist for all of them. As long as you know what hypothesis you test, you can find the right critical values. The built-in EViews procedures only test the simple hypotheses on the AR-term.


Return to “Estimation”

Who is online

Users browsing this forum: No registered users and 6 guests