Dear Amber,

Granger causality can be applied to non stationary data too.

I know methods for panel data, in particular this article:

https://www.sciencedirect.com/science/article/abs/pii/S0264999306000496

but there is a similar thread on RG where you can find useful answers to your question:

https://www.researchgate.net/post/Granger-causality-test-is-applied-on-non-stationary-data-or-stationary-data

Regards,

Piero

@Piero Esposito thankyou Soo much

See these links, please:

http://web.vu.lt/mif/a.buteikis/wp-content/uploads/2018/04/Lecture_07.pdf

https://www.researchgate.net/post/Granger-causality-test-is-applied-on-non-stationary-data-or-stationary-data

https://davegiles.blogspot.com/2011/10/var-or-vecm-when-testing-for-granger.html

Read this

https://davegiles.blogspot.com/2011/04/testing-for-granger-causality.html?m=1

Granger-causality testing in a VECM (that has short-run and long-run components) assumes all the data are stationary by either cointegration or differencing transformations. That is the DIFFERENCED variables and error-correction terms are stationary, the levels variables are I(1). If there is no cointegration the error-correction term can be excluded and testing is conducted by a Wald test in a stationary (difference) VAR. Alternatively, you can use the Toda and Yamamoto (1995) surplus lag Granger-causality test that uses nonstationary data. See Dave Giles blog (as Alhassan suggests) for a discussion of this - the link is given below. https://davegiles.blogspot.com/2011/04/testing-for-granger-causality.html?showComment=1320248137553#c4210543007105661619 This method means you do not need to consider the notions of long-run and short-run Granger-causality. This is useful if you simply wish to know whether Y Granger-causes Y for example. In a VECM long-run Granger-causality is tested using the t-ratio on the error-correction term in each equation. Short-run Granger-causality uses Wald tests to set the coefficients on all lagged differences of on variable to zero in an equation. In EViews I think this needs to be implemented using the make model/system proc.

First some comments on your statements on VECN

As per my knowledge, the steps to apply VECM is as follow

1. Check stationary (variables must he integrated of order 1)

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.

2. Check cointegration (Johenson if more than 2 variables, Engle-Granger if 2 variables)

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.