Everything i have said above can be summarized this way:

(a) one advantage of ARDL is that it avoids pre-testing of variabes but go ahead and test that the regressand is not I(0) and that other independent VARs are not I(2). However, since unit root tests are weak and because almost all times are treated as I(1) go ahead an run your data.

(b) since we do not want to rely so much on unit roots because of theier weakness run results with and without variable identified as I(2)

Assume the variable X

Then yoi can test Ho that the level is nonstationary I(1) against the Ha that it is I(0) i.e., stationary by ADF that is, Dx c trend Xt-1 Dx{1-5}

(b) to test I(2) against I(1) you test the first differences of X that is , DX

D2x c dx(-1) D2x{1--5}

First thing, ARDL model can be applied only if variables are integrated of order zero or one.

Regarding EG co-integration test, it can be done, but doing in multiple steps reduces degrees of freedom and is not much preferred in the literature. The better alternative would be johansen's test

Regarding the last question, if the variables are not co-integrated, the estimates are consistent even in the levels. you really don't need an ARDL model here.

You should use an ARDL because the unit root tests are weak. Second, by using ARDL estimator you will avoid the critistim of having no long-run values in your equations and if they are insignificant the two tests suggested by PSS (2001) will inform you. Note that ARDL doesn’t require pre-testing of the variables so that is to your advantage

Chuck A Arize Doesn't ARDL require you to at least ensure the variables are not integrated of order two?

Hello Guys,

Thank you very much. This is my first time doing time series and I am really unexperienced.

Could someone please provide a step by step guide on how to do this. I have access to both Stata 14 and Eviews 8.

Chuck, so if use ARDL whhat types of diagnostic tests should I be running. Also is there a paper on ARDL that explains all of that just so that I have some proper academic proof and it doesnt look like I have made it up.

Thank you.

You can't because the f-statistic given in the study of Peseran et al. (2001) will break down in the presence of I (2) variable. The appropriate method you can use is Toda Yamamoto Causality test.

As stated by Nithin M and James Tumba Henry, ARDL is inappropriate according to Pesaran, Shin, and Smith (2001). It is ideal when the variable are integrated solely of order one I(1) or a combination of order one I(1) and order zero I(0) . Thus, if the variable is a combination of I(1) and I(2), the appropriate method is the autoregressive model but Toda Yamamoto Causality test as suggested by James is also only appropriate when the variables are I(0) and 1(2). Try the Johansen's test as recommended by Nithin.

Nithin M

Yes, it does but most variables are 0=

Chuck A Arize

Your position of ensuring that the regressand is not I(0), when the variables are a combination of

I(1), I(0) and I(2) is a welcome development and open to further research and affirmation.

Thanks for demystifying some of these issues and for being at the forefront in making meaningful contributions.

No, you can't because the assumption of ARDL is variables must be integrated of order I(0) and I(1). if all variables are I(2) you can apply VAR.

You can run ARDL model when variables are I(0) and/or I(1) but they should not be I(2).

Everything i have said above can be summarized this way:

(a) one advantage of ARDL is that it avoids pre-testing of variabes but go ahead and test that the regressand is not I(0) and that other independent VARs are not I(2). However, since unit root tests are weak and because almost all times are treated as I(1) go ahead an run your data.

(b) since we do not want to rely so much on unit roots because of theier weakness run results with and without variable identified as I(2)

When unit root tests suggest variables are I(2) it is quite possible that this is due to the well known low power of such tests, where low power essentially means the tests tend to over reject the true lower order of integration null and incorrectly suggest a higher order of integration. Hence, variables that are I(1) are often suggested to be I(2) by such tests. Given this genuine problem with unit root tests it is advisable to consider the possibility that a finding of I(2) is due to low power and the variable is actually I(1). If the variable is actually I(2) this will likely be indicated by tests rejecting cointegration and/or yielding theoretically implausible results. Hence, as Chuck suggests, try applying cointegration tests both including and excluding variables indicated as I(2) by the unit root tests and assess the results.

I believe Chris Stewart's statements are correct and helpful.

Chuck A Arize Gabriel Efe Otolorin thank you very much for the information. My age dependency ratio is the only I(2) variable. Can you please give a reference for papers that argue the point that an I(2) variable can be used in an ARDL as long as the regressand is not I(0)?

Thank you very much

According to the Johansen cointegration test (which I do not believe is applicable) my there is a maximum of two cointegration equations. However, the Engles Granger two step test shows that the variables are not cointegrated. Am I right in thinking that the test should be applied to the level form of the variables?

The Engle and Granger test for cointegration will typically be based on I(1) variables, however, if two I(2) variables included as explanatory variables cointegrate such that there linear combination is I(1), for example, they can be included in the long-run model and can potentially cointegrate. On ARDL modelling, I(2) variables should not be included. However, the point is that variables that appear to be I(2) according to a unit root test may not really be I(2). They may actually be I(1) and the unit root test incorrectly suggests they are I(2) due to the well know problem of low power. Low power means unit root tests have a tendency to suggest variables are a higher order of integration than they really are. I have invoked this argument in the following paper that is available on line (let me know if you want a copy of this paper): Goda, T., Stewart, C. and Torres García, A. (2019) ‘Absolute Income Inequality and Rising House Prices’, forthcoming in Socio-Economic Review.

Chris Stewart thank you very much for your answer. I have further explored the problem with unit root and have discovered that Household Savings as a % of GDP is an I(1). I am frankly quite surprised to have discovered that the young dependency ratio is an I(2) variable. Unfortunately there is no way for me to drop or replace it because it is vital to my study.

So if the variables are cointegarted that means that the unit root incorrectly shows that the variable is I(2).

I am currently learning how to use Eviews to conduct a bound cointegration test.

If my variables are cointegrated I will carry on with estimating a ECM.

However, if they are not is my research basically worthless?

Yes, thank you very much I would love to have a copy of your paper.

Kristian, a finding of no cointegration is as interesting as a finding of cointegration. With research we should not think that we have to justify preconceived views or support theories. Finding evidence against them is as informative as finding evidence in their favour. You may want to look for robustness in your results and try different cointegration tests.

The easiest way for me to send you the paper discussed previously is for you to request it. You can do so from the page accessible from the following link.

Article Absolute income inequality and rising house prices

Good luck with your research.

Chris,

Thank you very much for the reply. You are a life saver. I have opted to test for structural breaks. As I dont know the exact date i have chosen the multiple break points. According to that my model has 5 breaks: 2003 1990 1978 2009 1997, with 1990 and 2009 being significant (after creating the dummies). Can I still construct an ARDL model and perform a Bound cointegration test? Is this the proper way to solve breaks?

Thank you