Granger causality can be conducted for bivariate time series or multivariate time series, to test for a relationship - one sided or two-sided. VAR models simultaneous relationships and may not be applicable for one-sided relationship. If your question is that you have evidence of one-sided relationship using Granger, do I need a VAR to model the relationship? A VAR has other strengths (tracing shocks to the system and to see whether it is stable) other than modelling such a relationship. It also depends on number of observations given your 5 independent variables which will affect your df.

Since you have a number of explanatory variables, its better to use VAR and check cointegration and apply VECM (reveals short and long run relationship). If the variables are stationary at different levels you can also use ARDL.

Mousumi Bhattacharya

Thank you for your answer,

So all my variables are stationary at I(0). Can I use VECM directly or first should I use VAR ?

Since your variables are stationary, you can use VAR directly.

VAR and other traditional econometric technics already have done in this topics. In my opinion, you must try other flexible methods such as state-space Kalman filter, threshold models.

If all variables are I(0) then you should go for VAR rather than VECM because VECM is feasible if cointegration exist among variables and cointegration should be checked only if all all variable are I(1)

I find it hard to believe that so many macroeconomic variables or their logs are stationary. Are you using rates of change. I would think that the reit index and the levels or logs of your macroeconomic variables are non-stationary. Is there a cointegrating (long run equilibrium) relationship or relationships between the levels of the variables. If there is VAR analysis between the returnsand the first differences or the other variables is misspecified and not valid. You then need to use VECM analysis.

If you have non-stationary variables you need to modify your Granger Causality Tests. The options are well documented in Lütkepohl (2005), New Introduction to Multiple Time Series Analysis.

The mechanics of Granger Causality are covered well in many introductory and intermediate textbooks. They often do not include a good discussion of the validity of such tests. If you have three variables x, y, and z (all possibly multivariate) a test that y Does not Granger cause x is a test that certain coefficients are in the var containing x, y, and z are zero. This is subject to an economic argument that all the relevant information is included in the VAR. If z is omitted you may get false causality. The idea of Granger Causality using a 5 or 6 variable variable VAR or VECM in conjunction with bivariate tests is definitely not valid. If the tests contradict one another only those based on the larger system are valid. If they do not contradict one another why do the bivariate tests

It has been suggested that you use the ARDL methodology. This requires certain exogeneity conditions to be satisfied and that there be only one cointegrating relationship between the I(1) variables.

You have chosen a difficult path to follow. You probably need to work jointly with someone who is an expert in this area. If this is a part of a thesis I would recommend that you talk to your supervisor and seek advice on exactly what is required. Are you expected to understand everything that I have outlined above or is some mechanical application of something like Granger Causality sufficient.

If your variables are stationary its better to use VAR and make cointegration test and apply VECM.

Anvar Kobilov If the variables are stationary then cointegration tests and VECM (Johansen) analysis do not apply. Stationary variables can not be cointegrated.

The stationarity of the REIT Index return is expected (since constructing a return series from price series involves logged differences). However, the stationarity of all macro variables is surprising! Any way, as stated by John C Frain, the use of cointegration and VECM is ruled out. So, you are left with VAR. The use of VAR requires making a distinction between endogenous and exogenous variables. Even though there are data based tests of exogeneity, it is better to consult economic, financial, etc. theory to distinguish between exogenous and endogenous variables. If all of your explanatory variables are exogenous, then VAR and two-sided Granger causality analysis are also ruled out (the dependent variable can not Granger-cause an exogenous variable). The only option? OLS!

Granger causality and VAR model can be used together for time series when t-test is used. Granger causality is a causality relationship between the lags item t-1, t-2, ..., t-q and the current item t. The vector auto-regressive model (VAR) is the original model of Granger causality. However, VAR is used for a long term causality, whereas VECM is used for a short term causality.

If variables are stationary you can apply Granger-causality testing in a stationary VAR. If the variables are nonstationary and not cointegrated you can difference the variables and apply Granger-causality testing in a stationary VAR of the differenced variables . If the variables are nonstationary and are cointegrated you can apply Granger-causality testing in a VECM (that has short-run and long-run components) that assumes all the data are stationary by either cointegration or differencing transformations. If there is no cointegration the error-correction term can be excluded and testing is conducted by a Wald test in a stationary VAR. Alternatively, you can use the Toda and Yamamoto (1995) surplus lag Granger-causality test that uses nonstationary data. See Dave Giles blog 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.