I think that you can transform it all I(0) so stationary then you estimate VAR

Or you can fit a multiple regression without talking about stationary of variables

You may want to consider the original assumptions about the time series properties of X, Y and Z were in accordance with economic theory.  

Please let me recommend this research:

Conference Paper Is Cash Dividend an Everlasting Stimulus? Impact of Cash Div...

We used the AB method for the situation when none of the variables is I(2) or higher.

@Andrey Davydenko please can you send me the full paper. I just saw an abstract. Thanks

It was an ePoster presentation. A paper will be available later. At present only this abstract and an ePoster is available:

Poster Is Cash Dividend an Everlasting Stimulus? Impact of Cash Div...

In general, we used this approach 1) use unit roots to understand there are no I(2) variables, 2) apply the AB estimator in R.

One really needs to know the nature of the model that you are estimating. You can always convert an I(0) variable to I(1) by integrating it. Say, have a series of total equity returns which are usually I(0). Total equity returns are simply the first difference of the log of the equity price which is I(1). Thus you can convert total equity returns to an I(1) equity price series. Inflation is often I(0) and can be converted to a price index in a similar way by integrating.

Thus you have the option of integrating I(0) series to I(1) or differencing I(1) series to I(0). What is appropriate depends on the nature of the economic model that you are estimating.

Autoregressive Distributed Lag Model (ARDL) is one of the time series method to due will mixed result of integration order of stationary test. In other words, all variables are stationary at different level such as some are I(0) and some are I(1) may proceed to ARDL model. If the cointergration bounds test shown significant which implied that the estimation model is not spurious.

Wong Vui Ken I think that you are thinking about Pesaran's ARDL model and the bounds test. In this case, the dependent variable is I(0). This type of ARDL model is not appropriate.

Only I(0) variables or first differences of I(1) variables or cointegrated groups of I(1) variables can be used to explain I(0) variables. You need a lot more economic theory and econometrics to support such a system.

If I have misunderstood your answer could you, please, clarify.

With the order of integration mentioned (i.e. a mixture of I(0) and I(1), ARDL methodology is suitable for your study. Here, you confirm existence of long run relationship (cointegration) through Bounds Testing.

Emmanuel Ikpe Michael As I have already stated the dependent variable is I(0). ARDL bounds test is totally inappropriate.

@John C Frain , I am modeling the health status and health expenditure nexus. My dependent variables life expectancy and infant mortality seems stationary at level. Although , I tried to further estimate this using ardl ingnoring the stationarity of dependent variable just to confirm the degenerate dependent variable assumption. And which i confirmed as the t stat for the dependent variable under the bound test is less than I(0). I would have thought about using the Mcnown bootstrap ardl which seems to be robust but code is only limited to 4 variables for now and I have usually seen it been used in panel data analysis.. While my work is time series in nature. Although i believe the bootstrap ardl can be used in times series analysis too.

Dear Hamid,

In a situation of different order of integration, panel ARDL is applied to derive a lo G and short run estimate of the analysis. ARDL is still one of the time series method used in the case of a mixed order of integration.

But with your recent point, Yes, the bootstrap ARDL can be used but you need to download journals for clarifications.

Regards

@ Kehinde Mary Bello , thanks. But my work is a single country estimate, panel ardl might not be appropriate. Besides, I believe perhaps the same rule applied to panel ardl when the dependent variable is I (0).

Hamid,

Sorry about that. In that case, ARDL is applicable in time series analysis. You can use ARDL since the variables are of different order of integration for time series analysis and then inculcate your Bound test.

Hamid Muili Sorry for not getting back to you sooner. You have chosen a difficult topic. As I do not have a detailed knowledge of your economy and your health system some of my comments may not be relevant.

I hope that these comments are of some use. When your data is insufficient you might better arguing with some graphs and regressions with I(0) variables. Talk to your supervisor to check what is expected.

you can use ARDL model

use the bounds test using the ARDL approach

Timothy Tyona and Folorunsho M Ajide The PSSS ARDL approach and the bounds test may be appropriate in certain cases where some variables are I(0) and others I(1), there is only one cointegrating relationship and certain exogeneity assumptions are satisfied. It is not applicable when, as here the dependent variable is I(0). Please read the original PSS article which explains why this is so. The bootstrap idea is just a refinement of the bounds test.

@ Folorunsho M Ajide, just as Prof John C Frain has noted, BARDL is just a modification of the oriinal PSS ARDL. the same rules still applies to boostrap ARDL. In the later, it will show you there's no co integration and the nature of the non cointegration. Perhaps a degenerate case 1 or case 2. While this might not be very clear in PSSARDL for beginners in econometrics..