Cointegration - Science topic

the pre-estimation condition is the presence of endogeneity in the data set

Johansen test of cointegration is all about the determination of the existence of long run relationship amongst variables captured in an econometric model. The condition is that if there exist alleast one cointegration at both trace and max. eigen test. However if there exist atleast one cointegrating equation at at any of the test, we can accept the existence of a long run relationship

No, Johansen cointegration is used when series are non-stationary at levels but stationary at first differences. If your price series are already stationary at levels, cointegration analysis is not applicable.

Quantile cointegration estimates assess the relationship between time series at different quantiles rather than just the mean. This approach helps identify how cointegration varies across different points of the conditional distribution, offering a more nuanced view of long-term relationships in the presence of non-constant volatility or asymmetric effects.

Chuck A Arize The eigenvectors or equivalently the characteristic roots of the Companion Matrix of a VECM determine its "stability".

If the roots are outside or on the unit circle ( alternatively if the eigenvectors are inside or on the unit circle then the process is non-stationary but "stable". By stable I mean that it converges to an equilibrium after a shock.

If the roots are inside or on the unit circle ( alternatively if the eigenvectors are outside or on the unit circle then the process is explosive.

It is possible that there is a form of overshooting in one of the equations in a VECM (positive coefficient on the ecm). If the system is "stable" the other equations (including the "short-term" effects) may still restore the new equilibrium.

Your suggestion regarding "incorrect signs" appears on many internet forums. It is not correct.

To replace missing data in a time series using EViews, you can follow these steps:

1. **Open your time series data in EViews**: Load the data into EViews and make sure the variable with the missing data is selected.

2. **Identify and mark the missing values**: In EViews, you can identify missing values by looking for the "NA" or "?" symbols in the data. You can also use the "View" menu and select "View Data" to see the data in a spreadsheet-like format, where missing values will be highlighted.

3. **Choose a method to replace the missing values**: EViews provides several options to replace missing data, including:

- **Mean/Median Substitution**: Replace the missing values with the mean or median of the non-missing values.

- **Linear Interpolation**: Replace the missing values by linearly interpolating between the nearest non-missing values.

- **Time Series Modeling**: Use time series models, such as ARIMA or Exponential Smoothing, to estimate the missing values based on the patterns in the available data.

4. **Replace the missing values**: Once you've chosen a method, you can use the "Fill Missing" command in EViews to replace the missing value.

5. **Verify the results**: After replacing the missing values, review the data to ensure that the substitutions are appropriate and do not introduce significant biases or distortions.

To apply the Kao Residual Cointegration Test in EViews:

Yes, you can check the stability of the cointegration relation using the Hasza and Johansen recursive method in EViews.

When variables are integrated in different orders (e.g., some are integrated of order 1, I(1), and others are integrated of order 0, I(0)), the appropriate cointegration approach to use is the ARDL (Autoregressive Distributed Lag) model.

ARDL models can accommodate variables with different orders of integration by including both level and first-difference terms in the regression equation. This approach allows for testing cointegration among variables with mixed integration orders and provides robust results under various scenarios.

In summary, ARDL models are suitable when you have a mix of integrated and non-integrated variables and want to test for cointegration relationships among them.

please check cointegration test and if all your variables are cointegrated simply use VECM.

You can forecast one variable of a Vector Error Correction Model (VECM) using external forecasts of the other two variables by incorporating these forecasts into the VECM equation and solving for the variable of interest.

After performing a stationary test for your data analysis using the ADL model, you have found that the dependent variable and 6 out of 8 independent variables are stationary only in their differences, while the other two are stationary in levels. In this scenario, you can proceed with modeling your data using an Autoregressive Distributed Lag (ADL) model.

Adam Tomko Moges Mengstu Kassaw Srk Haqbin Benjamine Gaspar Miku The ADL model is suitable for situations where variables exhibit different stationarity properties, such as some being stationary in levels and others in differences.The ADL model allows for the inclusion of lagged values of both the dependent and independent variables, accommodating the mixed stationarity properties of your variables. By incorporating lagged values of the variables that are stationary in differences, you can capture the short-term dynamics and relationships in your data. At the same time, including the variables that are stationary in levels enables you to account for the long-term equilibrium relationships.

This approach aligns with the flexibility of the ADL model, which can handle variables with diverse stationarity characteristics, making it a suitable choice for your data analysis scenario. By appropriately specifying the model with the lagged terms of the variables based on their stationarity properties, you can effectively capture the dynamics and relationships within your dataset. Adam Tomko

there is option in the upper menu you can run from there no need for the command

Yes, it is possible to skip it.

Since your dependent variable (CO2) is integrating at level (1) and all other variables are have a mixed order of integration, it is not advisable to use Pedroni and Westerlund cointegration tests. Because these two cointegration tests can only be used when DV is integrating at 1st difference and all other independent variables may be of I(0) or I(1) order. So, you can go for PMG-ARDL which is applicable in your case.

Second thing is that, some of your variables are integrating at 2nd difference. So, it better to drop those variables and use only use those variables that are integrating at most at I(1). You can refer to this article

Do you find any solutions? My model has 11 explanatory variables, I also faced same situation.

Sonia Bibi

I Do not have, but you can use a free version of GAUSS available for students called GAUSS Light 1. It has a maximum matrix size of 10,000 elements, no multi-threading support, and no debugger. You can purchase pre-written, customizable GAUSS Application Modules separately for an additional fee.

Cointegration analysis requires data to be integrated of at least order one (be nonstationary). If data are stationary (integrated of order zero) there is no need to apply cointegration analysis because the data cannot be cointegrated. This is because cointegration means that the linear combination of variables has an order of integration below that of the variables themselves. For example, if Y~I(0) and X~I(0) their linear combination cannot have an order of integration below 0 and they therefore cannot be cointegrated. Nevertheless, the model involving only stationary variables may still exhibit autocorrelation and need a dynamic specification (including lags of variables) that has a static long run solution (essentially obtained by removing time subscripts). However, this long run (equilibrium) solution will not be a cointegrating equation.

Try this;

xtcointtest westerlund Y X1 X2 X3

xtcointtest westerlund Y X1 X2 X3 , trend

A time series is I(d) if it is

Two I(d) time series X_t and Y_t are cointegrated C(d, r) if there exists a linear combination of X_t and Y_t such that Z_t = X_t + a Y_t is I(r) where r<d.

Two I(1) time series X_t and Y_t are cointegrated if a linear combination of X_t and Y_t exists, such that Z_t = X_t + a Y_t is I(0) stationary.

Note that a non-stationary time series is not necessarily integrated of any order. For example, it is often found that real GDP is nonstationary. Log(real GDP) is also nonstationary. The first difference of Log(real GDP) is usually found to be stationary and therefore Log(real GDP) is I(1). If this is so real GDP is not integrated of any order. However, applying unit root tests may imply that it is integrated of high order. Such a result is spurious.

An I(3) variable can not be an explanatory variable for an I(1). An I(1) variable can not be an explanatory variable for an I(3) variable. An I(3) variable can not be cointegrated with an I(1) variable.

If these points are not clear to you and you wish to work with such series you should attend a set of relevant time series lectures or consult a time series book such as Enders (2014), Applied Econometric Time Series, Wiley.

I would think that economic theory and common sense might imply that the log of the exchange rate might be I(1). (Asset pricing theory ?) I can not think of any reason why your interest rate is I(3). (I would not use the log of the interest rate?). Your result is almost certainly spurious. Are there any institutional or other factors that might cause discontinuities in your series? Is the 2-year bond market deep?

There are a lot of variables missing in your analysis. I suspect that the difference between the domestic and foreign bond rates may be important. The differences between domestic and foreign inflation may also be important. There may also be other domestic or external factors that may be important. Consider the following example. If foreign bond rates increase and domestic rates match them there should be no pressure on the exchange rate.

When there are multiple cointegrating equations, you can use vector error correction models (VECMs) to analyze the relationship between the variables. VECMs include both short-run and long-run dynamics and can be used to analyze the relationship between multiple variables1

To run an ARDL model from start to finish, you can follow these steps:

In summary, to run an ARDL model from start to finish, you can collect the data you need for your model, open the Eviews program, load the data you want to use for your model, click on the “Quick” menu and select “Estimate Equation”, select the variables you want to include in your model, click on the “ARDL” button to specify that you want to run an ARDL model, specify the order of integration for each variable in your model, and click on the “OK” button to run the model.

Yes, it is possible to do cointegration analysis for agricultural commodities that are available only for 2/3 months in a year. Cointegration is a statistical method used to test the long-term relationship between two or more time series1. It is commonly used in finance and economics to analyze the relationship between commodity prices and other variables such as supply and demand, inflation rates, exchange rates, etc.

In fact, a study conducted by Allen et al. confirmed the cointegration relationships among agricultural commodities (including corn, wheat, and sugar), ETC

It is merely a scale-localized version of the usual cross-correlation between two signals. In cross-correlation, you determine the similarity between two sequences by shifting one relative to the other, multiplying the shifted sequences element by element, and summing the result.

Wavelet cannot be used to test for cointegration

Hi Welani Khondowe Muhammad Kazim Jafri ,

Thank you for your responses. I reduced my sample data points and tried again. Because my dataset included data from the covid 19 period. So I removed covid 19 affected period from my dataset and run the unit root again. Then all the log forms of variables were stationary at level 1 (I1).

Thank you both of you very much.

Cheers!!!

The ARDL bounds test assumes at most one long run levels relationship. It does not test for multiple long run relations. The Johansen test can test for multiple cointegrating relationships. The difference is that the Johansen procedure assumes all levels variables are I(1) whereas the ARDL procedure assumes the dependent levels variable is I(1) and the independent variables can be I(1) or I(0). Using both tests may be useful if there is uncertainty over the orders of integration of the levels variables and the number of long run relations. If you are certain all levels variables are I(1) you only need to use Johansen. If you are certain there is one long run levels relationship and uncertain over the independent variables' orders of integration you only need to use the ARDL test.

I am using xtwest stata command it has limitation can not use more than 6 variables, in a model.

A vector of I(1) variables yt is said to be cointegrated if there exist at vector βi such that βiyt is trend stationary. If there exist r such linearly independent vectors βi,i= 1,...,r, then yt is said to be cointegrated with cointegrating rank r.

Hi Pushp Kumar

I am looking for the stata commands for CUP-FM and CUP-BC estimation like you. Have you had them? If so, can you share with me?

Thank you

Zubair Ashraf

The comparison between the two models may provide insights into how the variables respond to short-term shocks and how they adjust back to their long-run equilibrium relationships I think.

Hello Adam Roble ,

As your variables are stationary at level I(0), then you should go for VAR model directly after selecting the lag length. VECM is not ok for your dataset.

You can use Johansen cointegration test when all variables are stationary at first difference I(1). When Johansen test result shows cointegration among variables only then you can run VECM model.

And you can also conduct Granger Causality test to find out if the lag values of independent variables affect the endogenous variable or not.

If series are of same order of integration, we use cointegration otherwise ARDL. Second difference is rare. According to many econometricians, 2nd difference is to be avoided.

So far your variables are concerned, 3 rates (percentages), 1 index (ratio), Govt effectiveness (dummy or berometric var) and 2 $ values (GDP/Capita and remittance).

Ratios are done max at first difference, you better look into the data.

take natural log (ln) of the $ values, it will serve the purpose.

Joao Carlos Souza Marques There is nothing about 2nd generation panel cointegration mentioned.

This is a difficult problem. I will try an explain some of the points using a 4-variable system with 2 cointegrating vectors.

1. Say you have 4 variables (x1, x2, x3 and x4) and the Johansen test imp[lies that you have 2 cointegrating relationships.

2. The Johansen methodology then estimates two cointegrating vectors which I will write as

ecm1 = a11 x1 + a12 x2 + a13 x3 + a14 x4, and

ecm2 = a21 x1 + a22 x2 + a23 x3 + a24 x4.

The problem is that any two independent combinations of these two ecm's is also a set of cointegrating vectors. The problem is that econometrics can not choose the appropriate two ecm's from the infinity of ecm's available.

3. At this stage you need to understand the concept of identification. If you are not familiar with identification read the section in your econometrics textbook on identification in simultaneous equations.

4. An example of identification in the ecm's at 2 above would be to specify in ecm 1 that the coefficient of x4 be zero, and the coefficient of x1 be 1. In ecm 2 you might insist that the coefficient of x1 be zero and that of x2 be 1. This gives you two ecm's

ecm12 = x1 +b12x2 + b13 x3

ecm22 = x2 +b22x2 + b24 x4

The identification restrictions are obtained by economic argument and do not require any tests. Your software manual should explain how to impose the restrictions on the system.

5. You can now test what is known as overidentifying restrictions (for example that b24 = 0 if this is hypothesized by your economic theory).

The Johansen test and estimation methodology is based on some very complicated linear algebra and gives exact algebraic solutions to the maximum likelihood problem. I would generally recommend Juselius (2006), The Cointegrated VAR Model: Methodology and Applications, OUP and Kilian & Lütkepohl (2017), Structural Vector Autoregressive Analysis, OUP as covering a lot of this material. These are graduate-level texts. If you master this you will have made great progress.

It is also possible to estimate models such as these using numerical methods to solve the maximum likelihood problem rather than the exact solutions proposed by Johansen. I presume that this is the MECM method proposed by Othmane Lamzihri. There is coverage of this methodology in Martin, Hurn & Harris Econometric Modelling with Time Series, CUP. This is an easier approach to VECM and MECM estimation but it is not as comprehensive. It contains a lot of sample programs.

Both methodologies should give the same results when used on the same specification. The Johansen methodology requires fewer computer resources. The Maximum likelihood Method requires some programming. However, It may be easier to implement some model restrictions in MECM.

You say

How do you come to this conclusion? I suspect that Eviews has calculated t-statistics for these variables. These t-statistics do not have a standard t-distribution. P-values for these statistics calculated in this way are not valid indicators of significance.

My reading of your result is that there is no cointegration. Perhaps you should consider your underlying model

In small samples the distribution of the residuals of a model need to be normally distributed for hypothesis tests on the coefficients to follow the standard distributions. In large samples the Central Limit Theorem applies and the coefficients follow conventional distributions despite the residuals not following a normal distribution. However, the tests for a long run levels relationship in an ARDL model are nonstandard. Nevertheless, my understanding is that in large samples the ARDL model can have nonnormally distributed residuals and the simulated nonstandard critical values will be valid. However, this will not be the case in small samples. Others may have more information on whether the nonstandard critical values are valid in large samples when the ARDL model's residuals are non-normal.

The difference between R squared in the ARDL model and R squared in the bounds test is that R squared in the ARDL model is about the rubostness of the overall model result and not about the robustness of the bounds test result only. This means R squared in the ARDL model will tell you how much the variability in Y or Ys (your dependent variable/variables) is/are explained by the ARDL model given Xs variables (your independent variables). On the other hand, R squared in the bounds test is specifically about the bounds test result within the ARDL model and not about the robustness of the overall model result. You need an ARDL model first to have a bounds test but not a bounds test to have the ARDL model. I hope it helps you.

I presume that you have real GDP and your energy consumption is in volume terms and that you are working with the log of both variables.

I would suggest that you go to your textbook and see if you can replicate the results of a lag selection example in the test book. It is difficult to give you a diagnosis without your data and your program. Otherwise, try a different econometric package (e.g. https://gretl.sourceforge.net/ which is free and user-friendly).

Treating 4 as maximum lags your criteria must be estimated using observations 5 to 29 as independent and 1 to 4 as lagged variables only, Treating 8 as maximum lags your criteria must be estimated using observations 9 to 29 as independent and 1 to 8 as lagged variables only, etc.

In ADF tests the maximum lag is often taken as

[the integer part of 12*(T/100)^0.25] which is 8 for 29 observations. See Hayashi, Econometrics page 592 and references therein. Many econometric packages used to use this as a maximum lag for determining lag length in this and other occasions. I would hope that with 29 observations it would specify a smaller number of lags as appropriate.

How can you justify economically that eight lags could possibly be valid? to add an extra lag to carry out this test. If you do not have cointegration then you use standard Granger tests and VAR in first differences. You will need strong economic arguments to justify the assumption that there are no other variables that are impacting both GDP and energy consumption. If there are such variables your test will not be valid.

How can you justify economically that eight lags could possibly be valid? There is something wrong with your model. The eight lags may be adjusting for autocorrelation caused by misspecification or an omitted variable. Unless there is something wrong with your calculations you need to rethink your model.

Yes, you can use it.

co integration analysis it is important to do unit root analysis to identify the stationary and order of integration. Using Augmented Dickey Fuller tests and KPSS Test. The results reveal that all the series are non stationary at levels as test statistics are greater than the critical values. However by taking the first

difference all the series are found to be non-stationary. then by taking the second order differential all series are found be Stationary. Thus the null hypothesis is rejected and the log values of future, spot prices are found to be stationary at Second difference and are integrated in the order of two.

You can try AMG and CCMG for robustness.

Yes. You may run Granger causality test at level to find out the causal relationship.

Thanks for these links!

I don't think that there is an easy answer to your question. The problems you discuss are covered in Juselius (2006), The Cointegrated VAR Model, Oxford. When I last used Eviews their Johansen routines would not have covered all the routines in this book. That was some time ago and things may have changed. Cats in Rats (estima.com) or the equivalent in Oxmetrics were better. For a more modern survey, you might look at Killian and LUtkepohl, Structural Vector Autoregressive Analysis, Oxford. These are graduate-level tests and are not easygoing.

You can try Kuriyama (2016) cu sum quantile cointegration test.. Check the link for supplementary materials

Dear Baylie,

Interesting query. I have always utilized ARDL bound test to assess presence/absence of cointegration relationships among the identified variables (single cointegration).

Ateeb Akhter Shah Syed This is a tough question. First, you must understand the concepts of identification in a structural economic system of equations. This is covered well in many introductory and intermediate textbooks. Before you do any unit root tests or cointegration analysis you should consider what your theory and common sense say about the integration state of your variables and ask what cointegration equations you expect to find in your analysis. You then look to see how you can identify the system using theory and common sense.

When you have completed your examination of the economics of the system You can then use the Johansen methodology to estimate and test your model. Now say your econometric analysis implies that there is more than one cointegration vector. The trouble with Johansen is that it only estimates the cointegration space of the cointegration vectors. For example, if you have three cointegrating vectors then any three independent linear combinations of the original cointegrating vectors are also valid cointegration vectors. You must use your economic theory from your preliminary analysis of the model to select three unique cointegrating vectors. For a brief explanation have a look at Martin, Hurn, and Harris (2013), Econometric Modelling with Time Series, Cambridge page 682.

Some but not all time-series packages have the facilities to manage a lot of these calculations. CATS in RATS (https://www.estima.com/) or CATS in Oxmetrics. These are based on the Juselius book. Check your own software and see how far it goes.

If you need to do advanced work in this field you will need to understand what is in the Juselius book and in recent research in this field (see Killian and Lutkepohl (2017), Structural Vector Autoregressive Analysis, Cambridge). If you need to do less, consult your tutor, supervisor, or lecturer to see what he thinks is appropriate for your existing knowledge of economics, econometrics, and computing. This is a difficult topic and you could spend a lot of time learning how to do it.

Dear Waseem Baig,

You may explore ARDL and non-linear cointegration techniques.

Sorry for the typo- the corrected version

Cointegration is primarily used to identify possible causality among the variables. It rules out spurious relationships. Direction and strength can be evaluated from the coefficient estimation model.

Hi, thank you for replying.

I thought that could be the problem but when i test the model with my full sample with 4165 observations i get the same problem. I attached the file bellow with the full sample

Mr a. D.

The ECT(-1)os always the lagged value of your dependent variable.

Regards

Watching this video might help;

Dear Brajesh ji

please see this article Augmented Reality is Eating the Real-world! The substitution...hope it helps

You can go to the Robust approach, you may use ARDL as well as VECM and accept the model which provides more accurate results.

Emmanuel Gabreyohannes Can you provide a literature justification that the predictors need not be stationary in logit and probit models?

Dear Devesh ji,

Selection of DV and resulting model is primarily a researcher's choice which is subject to following :

#You get a negative ECM (in your case)

#The necessary prerequisites are fulfilled.

#The short run and long run makes sense to what you are trying to convey through your research.

#Validate the underlying relationships of DV and IVs through different modeling techniques.

With best regards

First some comments on your statements on VECN

The Johansen methodology can be extended to include I(0) and I(2) variables. This is not covered in introductory textbooks or in many econometric packages. See Juselius (2006) The cointegrated VAR model for details.

Johansen can be used if there are one or more cointegrating vectors. Engle-Granger can be used when there is only one cointegrating vector. Engle-Granger can be used when there are more than two variables. Johansen may be better if you have two variables. If one of the variables is not weakly exogenous a single equation will miss part of the adjustment process.

Before you do any VECM econometrics it is important that you have an econometric model that includes indications of the degree of integration of your variables and indicates the nature of any cointegration relationships that you might find. You will need this to enable the identification of your cointegration relationships. Applying VECM recipes to a data set and then trying to provide economic explanations of your result will usually lead to spurious results.

If your data are I(0) Granger causality can be tested with the standard VAR methodology

If your data are I(1) I would recommend that you consult Lutkepohl (2003), New Introduction to Multiple Time Series Analysis, Springer, pages 316-321. Granger causality is also applicable but is a little more complicated.

Be warned also that the t-statistic on an error correction term does not have a t-distribution, To test that such a t statistic is significant you can construct a Likelihood ratio test comparing the likelihood of the unrestricted model (relevant ecm terms included) with that of the unrestricted model (relevant ecm terms excluded). Significant ecm terms imply Granger causality through the error correction term.

Without knowing the nature of your variables and economic model it is difficult to answer your question. the following points should help

As long as the series are not I(2) you can use them in the ARDL model, this means you can employ I(0) or I(I) orcombination of the two.

best,

G K Zestos

Dear Ahamed.

For a robust result, you should carry out a cointegration test to verify if the variables are cointegrated before moving on to PMG/ARDL techniques.

Regards

Dear Puneet.

Why not consider using ARDL as recommended @Mwoya Byaro.

Regards

Dear Devesh Kumar Pant

If you are using time-series, you can identify the break years first. For this, you can use the Maki cointegration. After that you can apply the ARDL method where you can externally incorporate the break years to capture the effect of SB in your final model.

Dear Devesh Kumar Pant I think that it would be a great idea to replace the variable that is integrated to order 2 or higher and to find a substitute of that variable if that is not that excruciating.

Hi, you can find help from this source:

Dear Chellai.

Using Eviews.

* Import your data into Eviews

* Then select Group Statistics

*Then go to Quick

* Then click Johanson Cointegration test

* From the series list, list out your variables accordingly.

* Click OK

* From the Johanson cointegration test icon, adjust the lag intervals.

Then click okay for your result.

There is no specific icon for SVAR cointegration test.

Regards

Dear Zaki Farhana

I suggest that you first transform the series into log form and then check the degree of cointegration.

I agree with all comments made above by John C Frain

Let me add an obvious point he needs to check. The equation has no significant error correction term, even though he claims he has two vectors. In no case did the dynamics translate into the steady-state. Take out the trend variable and ensure that appropriate outliers have been handled with dummies vars, including seasonality, and avoid extreme models (i.e., without intercept and inclusion trend variable, Johansen 5).

For classic frequentist analysis (i.e, panel model & time series); depends on the hypothesis.

There is no rules of thumbs casted on stone, that a certain number of independent variables should be the minimum in exploring the links between dependent variables and independent variables. But having 22 observations are enough and have high degree of freedom to conduct the study. However, avoid including too many variables in the same model (i.e 7 variables) may cause multicollinearity.

You can also use Bayesian estimate, in which the small samples sizes can be simulated to larger sample by MCMC....

It is not clear, what you want to show by your analysis. Do you try to find an explanation for GDP (for forecasting or?) and trying to get rid of the disturbing effect of Covid or is the main goal to estimate the Covid-effect on the economy? For me it seems that you are not interested in an economic problem, but only want to get some exercise in econometric methods and programs. Your "model" (i.e. equation to estimate) seems to be

GDP = Function(Exports, Imports, Covid19-Dummy), where, I suppose, that Function is linear, but the variables are transformed (ln, differences, exp etc.?). Whatever these transformations, this is a rather strange model. It is neither demand nor supply side, and I cannot see any other theoretical base.

As GDP is - by definition - the sum of internal demand (consumption, investment, change of stocks)+exports-imports, there is a severe endogeneity problem (see John's contribution) - especially as imports can be assumed as highly dependent on GDP (via income and consumption or because they are inputs for the domestic production).

Following your response on the research interest through your research topic, then, it is imperative to know the basic purpose of cointegration test, regardless of whether panel cointegration or time cointegration.

Cointegration is use to test for joint stability or comovement of variables. Hence, the variable must be more than one. Second, the two variables must be in same order of dataset- whether time series or panel dataset.

Since your study objective consider multiple countries, then, convert the oil prices in time series to the stack/panel series. Then both panel variables can now under panel cointegration test.