UNIT ROOT TESTING ISSUES

[tomsmith]

Dear Tom,

While testing for a unit root, I have used both the @dfunit and @ppunit procedures but I am not sure I fully understand what the options are actually testing. For example, what is the difference in the actual hypothesis tests between the following commands (note IBM4 is just the name of the series).
@dfunit(ttest) IBM4 @ppunit(ttest) IBM4
@dfunit(nottest) IBM4 @ppunit(nottest) IBM4
@dfunit(nottest,trend) IBM4 @ppunit(nottest,trend) IBM

Are these joint hypothesis tests (Ho:(α,β,φ)=(α,0,0) vs Ha: (α,β,φ)≠(α,0,0) where α is the intercept and β is the trend component) or are they just simply testing for a unit root (Ho:φ=0 vs Ha:φ<0) in the presence of an intercept and/or a trend.

Note: The time series models with which I am trying to estimate can be described by:
ΔYt=α+βt+φYt-1+εt
ΔYt=α+φYt-1+εt where εt is iid white noise in both cases.
Also, φ=(ρ-1) where ρ is the original coefficient for the Yt-1 term.

Your help on this matter would be greatly appreciated,

Regards,

Tom

[TomDoan]

Dear Tom,

While testing for a unit root, I have used both the @dfunit and @ppunit procedures but I am not sure I fully understand what the options are actually testing. For example, what is the difference in the actual hypothesis tests between the following commands (note IBM4 is just the name of the series).
@dfunit(ttest) IBM4 @ppunit(ttest) IBM4
@dfunit(nottest) IBM4 @ppunit(nottest) IBM4
@dfunit(nottest,trend) IBM4 @ppunit(nottest,trend) IBM

Are these joint hypothesis tests (Ho:(α,β,φ)=(α,0,0) vs Ha: (α,β,φ)≠(α,0,0) where α is the intercept and β is the trend component) or are they just simply testing for a unit root (Ho:φ=0 vs Ha:φ<0) in the presence of an intercept and/or a trend.

Note: The time series models with which I am trying to estimate can be described by:
ΔYt=α+βt+φYt-1+εt
ΔYt=α+φYt-1+εt where εt is iid white noise in both cases.
Also, φ=(ρ-1) where ρ is the original coefficient for the Yt-1 term.

Your help on this matter would be greatly appreciated,

Regards,

Tom

The TREND options (DET=TREND is actually the newer and preferred way to write that, since it's what's used in more procedures), are for testing φ=0 in your form:

ΔYt=α+βt+φYt-1+εt

The options without TREND (DET=CONSTANT) are testing φ=0 in

ΔYt=α+φYt-1+εt

They aren't the joint tests. The TTEST form is (by far) the most commonly used; it uses the t-test statistic for φ=0 in the augmented regression for DFUNIT and an adjusted form of that for PPUNIT. The non TTEST form uses Tφ in the augmented regression as the test statistic for DFUNIT and an adjusted form of that for PPUNIT.

[T_FIELD]

Dear all,

Could you help me on Perron (1997)?

When using Perron (1997), are the distributions of the parameters on Tb a standard t-distribution?
To select the model among IO1, IO2, AO, I think we have to test the null of theta = o and/or gamma =0,
where theta is the parameter of DU=1(t>Tb) and gamma is that of DT=1(t>Tb)*t, 1(*) is index function.

I am more than happy if anyone gives me any advice.

T_FIELD

[TomDoan]

Use the @PERRONBREAKS procedure for that. It's included with RATS and described at

http://www.estima.com/forum/viewtopic.php?f=7&t=826

When you want help with a paper, please do not use references like Perron(1997)---use a full reference.