The variables are both I(0) which means using OLS will be appropriate instead of using the Johansen test. However, how can this OLS be applied into Granger causality to verify the short run relationship? Should VAR model or VECM be used?
Dear Yen
You can use Granger causality test for short - term causality test
In addition, you can use VAR with the impose response function to get more information
But, since both variables are stationary at level, so VECM is not applicable
Best
Canh
Dear Canh, Is there any need for further test since the series are stationary at I(0)? Eagle-grander test is meant for I(1) while if the series are stationary at I(0) and I(1) we can use BOUNCE Co-integration test by Pesaran Shin and Smith.
I am not sure if series that are stationary at I(0) can depict short run or is there any other further test?
If your series are I(0), so no need to go further, just OLS is to be applied. it is obvious that there is no non-stationary behavior in your variables, so it will be waste of time to find causality. There is no time variant mean, variance and co-variance of the series, so why u are interested in long run and short phenomena.
Just interpret ur results and conclude.
Hope it will help u.
Habib
Dear Yen,
you can device a SVAR model with short-run restrictions on your parameters and then use impulse response analysis OR you can go directly into Granger tests but you must be careful when interpreting your results. Especially using the word causality in connection to GC test might be a bit tricky.
"X is said to Granger-cause Y if Y can be better predicted using the histories of both X and Y than it can by using the history of Y alone."
The first option will allow you to exactly specify your equations in a VAR system and then obtain estimates via OLS (depends on what software you are using). Be aware of autocorrelation (nonnormality is statisticly fine, as well as heterogenity)
The second, using CG test will require you to test your data in levels (not differenced, log is probably ok).
Since your variables are integrated of the same order I(0), it is ok to use Johansen cointegration test, and given that your variables are cointegrated then you can set your model as ECM but not VAR. The short term impact represented by the significance of joint F test of the lagged differenced explanatory variables .
I don't understand why to test for ECM and co-integration if all the variables are I(0)?
Bcz OLS is the most appropriate tool to be applied. Variables are time invariant so is it good to forcefully make them time dependent
Granger's Representation theorm imply if variables are cointegrated it is required to set the model in ECM framework to avoid misspecification problem arising from first differenced series. Now, the question is, why we need to difference series if they are already stationary? some times the problem may deal with stock returns, or price change, so in that case it is important to use ECM, to avoid model misspecification problem and also to separate the long term from short term responses. As a result use of OLS and ECM or Granger causality are two separate things.
If one has two varaibles X and Y, where a causal relationship goes from X to Y, one can, I think, find out the direction of causality by statistical methods only if lags are involved, i.e. if changes in X precede changes in Y. I understand that if both variables are i(0), there can only be one simple lag (no distributed lag structure) or no lag at all. In principle, this should be an easy task. but, in practice, the data periodicity could be much long than the lag (for example: annual data with a lag of one week or so between X and Y). An additional problem is, that Y may be influenced by other variables, too.
here is a resource
https://towardsdatascience.com/macroeconomic-financial-factors-and-ordinary-least-square-regression-4831302e7b69
From an OLS regression, you can examine the coefficients of the independent variables to determine the short-run relationship. Specifically, in a time-series context, the coefficients of the independent variables represent the immediate impact (short-run relationship) of changes in the explanatory variables on the dependent variable.
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