Answering my own question,

When checking the code in the add-in, it seems like the critical values are fixed for only 60 observations (when comparing with the critical values in the original article, table 1, p362).

Therefore, one should not trust the presented critical values unless one has 60 observations as in the PPURoot-code.

Maybe it will be too complicated to update the program with new critical values, even if it works by just writing them directly into the code. However, in Perron's paper he have just the critical values for T=60, 80, 100 and infinity, and in some cases 70, 100 and infinity. I do not really understand why he chose these unusual values. Any ideas?

Are there any updates regarding these values?

Perron (1997), Journal of Econometrics 80 (1997) 355-385, Further evidence on breaking trend functions in macroeconomic variables.

## PPURoot (Perron 1997 unit root test)

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### Re: PPURoot (Perron 1997 unit root test)

Hello

Yes, Published critical values are for a sample size 60. When you install the program have access to the code, and you can modify it to include a new window that takes into account the other sample sizes ...

Regards

Yes, Published critical values are for a sample size 60. When you install the program have access to the code, and you can modify it to include a new window that takes into account the other sample sizes ...

Regards

### Re: PPURoot (Perron 1997 unit root test)

Dear Prof. Ibarra,

Thank you very much for your answer!

However, I have some questions regarding PPUROOT that I would appreciate if you would answer.

E.g. if one under the null hypothesis (H0) would simulate the following DGP with structural breaks... I do not get it (I use EViews syntax so that we do now need to deal with font problems in any formulas, and this is based on the formulas in the attachment):

SERIES Y=mu_sc+DVTB_ser+DVU_ser+Y(-1)+NRND

where the scalar mu_sc is equal to 1 this gives a drift, the series DVTB_ser is always zero except for at e.g. observation 51 where it is 1, the series DVU_ser is always zero except for observations after observation 50 which follow a @trend. However, if the single 1 is replaced by 0.5 in DVTB_ser, this will lead to a different statistical size when running y.ppuroot(lag=4, model=B)

However, if one would just run the following DGP (under H0): SERIES Y=Y(-1)+NRND then I would understand that one could get only one critical value. The problem is that it says in the instructions that we allow structural breaks under H0 (I understand this under H1, but not also under H0. I cannot see what one puts in a break under the H0, the magnitude of the break under H0 will give decide the value of the critical value.

(See the attachment over the formulas and notations used. It is a photo over this Perron's 1997 method (from Pattersson, 2000). It should not infringe any copyright rules since I am posting my own photo of only a part of a page).

In summary, if I change the magnitude of the impulse dummy from e.g. 1 to 0.5 this should change the critical value (the critical value that should give a statistical size of exactly 5%). Therefore, the empirical statistical size would be different from 5% when the value of the impulse dummy in DVTB_ser is changed.

I can see how critical values can be simulated when we do NOT have a structural break under H0 (or a possibly a structural break of known size), but not when having a structural break under H0.

- Or with what data generating process (DGP), and with which parameters, is the critical value simulated??? Please alter the code above so that I can see exactly how the DGP really looks like under the H0.

Here are the critical values from Perron (1997):

Thank you very much for your generous assistance!!!

Thank you very much for your answer!

However, I have some questions regarding PPUROOT that I would appreciate if you would answer.

**1.**I cannot see how the critical values (for the unit root coefficient) can be simulated for e.g. 100 observations, WHEN WE ALLOW FOR A BREAK UNDER H0. With no break under H0 and only a break under H1, then I understand - but not if there is a break under both H0 and H1. If we, under H0, have a structural break of magnitude 1, this will give a different critical value for the unit root coefficient, compared to the critical value in the presence of a break of magnitude 0.5. This would lead to different critical values for every structural break magnitude – break magnitudes which are unknown.E.g. if one under the null hypothesis (H0) would simulate the following DGP with structural breaks... I do not get it (I use EViews syntax so that we do now need to deal with font problems in any formulas, and this is based on the formulas in the attachment):

SERIES Y=mu_sc+DVTB_ser+DVU_ser+Y(-1)+NRND

where the scalar mu_sc is equal to 1 this gives a drift, the series DVTB_ser is always zero except for at e.g. observation 51 where it is 1, the series DVU_ser is always zero except for observations after observation 50 which follow a @trend. However, if the single 1 is replaced by 0.5 in DVTB_ser, this will lead to a different statistical size when running y.ppuroot(lag=4, model=B)

However, if one would just run the following DGP (under H0): SERIES Y=Y(-1)+NRND then I would understand that one could get only one critical value. The problem is that it says in the instructions that we allow structural breaks under H0 (I understand this under H1, but not also under H0. I cannot see what one puts in a break under the H0, the magnitude of the break under H0 will give decide the value of the critical value.

(See the attachment over the formulas and notations used. It is a photo over this Perron's 1997 method (from Pattersson, 2000). It should not infringe any copyright rules since I am posting my own photo of only a part of a page).

In summary, if I change the magnitude of the impulse dummy from e.g. 1 to 0.5 this should change the critical value (the critical value that should give a statistical size of exactly 5%). Therefore, the empirical statistical size would be different from 5% when the value of the impulse dummy in DVTB_ser is changed.

I can see how critical values can be simulated when we do NOT have a structural break under H0 (or a possibly a structural break of known size), but not when having a structural break under H0.

- Or with what data generating process (DGP), and with which parameters, is the critical value simulated??? Please alter the code above so that I can see exactly how the DGP really looks like under the H0.

**2.**Another thing, when checking the critical values at page 362-363 in Perron (1997) is it the “k(t-sig)” row that table one should use for getting the critical values? I get this impression by reading your pdf-documentation. Is “(a) Model 1” min t(alpha-hat) in Perron (1997) related to your Model A in y.ppuroot(lag=4, model=A)? Is “(d) Model 2” min t(alpha-hat) in Perron (1997) related to your Model B in y.ppuroot(lag=4, model=B)? Is “(g) Model 3” min t(alpha-hat) in Perron (1997) related to your Model C in y.ppuroot(lag=4, model=C)?Here are the critical values from Perron (1997):

**3.**Also it seems like your y.ppuroot(lag=4, model=**B**) corresponds to Patterson's (2000) Model**C**, and when using your y.ppuroot(lag=4, model=**C**) this corresponds to Patterson's (2000) Model**B**. Patterson (2000) is based on Perron (1997). Am I right? See the first attachment in this post with Patterson's formulas.**4.**What is the maximum lag that may be chosen by PPUROOT?Thank you very much for your generous assistance!!!

### Re: PPURoot (Perron 1997 unit root test)

We have daily data(all 7 days ) time-series and we are running PPURoot with

Break location = Trend

maximum lag length = 365

The results of add-in are:

structural break at 20-oct-2013

chosen lag length = 283

Is this approach of choosing maximum lag for daily data as 365 correct? and how do one decide on selecting a break location ?

Waiting for a reply

Regards

Akash

Break location = Trend

maximum lag length = 365

The results of add-in are:

structural break at 20-oct-2013

chosen lag length = 283

Is this approach of choosing maximum lag for daily data as 365 correct? and how do one decide on selecting a break location ?

Waiting for a reply

Regards

Akash

### Re: PPURoot (Perron 1997 unit root test)

Hi Akash

The choice of 365 days is correct. To choose the structure of the deterministic trend should be guided by the graph of the series.

Regards

The choice of 365 days is correct. To choose the structure of the deterministic trend should be guided by the graph of the series.

Regards

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