The tests that I need to conduct are:
1. Unit Root Test
2. Multicollinearity Test
3. Heteroskedasticity
4. Auto-correlation
5. Normality test
6. Granger causality
7. Regression
Is there a specific order in conducting these tests?
Next Question.
For unit root tests, if at level, the intercept and trend + intercept results differ (one is stationary while the other is non stationary)
Do i need to difference it? (A tutorial that I watched said that if all 3 do not give a definite answer then I should difference it)
Thanks.
Order of integration for linear regression of time series data follows certain rules. For instance, you are to firstly conduct a unit root test, it is the order of integration of your unit root test that predicts technique to be applied, if all your variables are integrated at level i.e. I(0), then you are free to proceed to ordinary least square method, after which you can perform some post estimation test such as collinearity, heteroscedascity e..t.c. However, some soft ware package quickly report multicollinearity at the first attempt especially STATA.
Yusuf Bat-Hef Basic Regression (OLS) is only possible when all your variables are I(0). (see good books on it). Therefore you need to run first unit root tests. You can check multicollinearty before going to model estimation. Very basic tool is to make correlation matrix of your variables. All other tests like normality (of error) and haterscedasticity can be checked after model formulation.
Now come to model selection.
1. If your all variables become I(1), then you can check cointegration for long run relationship. Tests are- Johansen Cointegration test and Engle-Granger error based cointegration test.
2. If long run relation exists, you can check short run relation through Vector Error Correction model.
3. Then you can test Granger Causality for causality analysis.
4. Suppose you don;t find cointegration then how can you check causality ??
i recommend to you to check Toda-Yamamoto causality test. This test will be showing causality irrespective of possible cointegration and order of integration (whether I(0) or I(1) but not I(2))
5. If in unit root test, you have mixture of variables i.e. I(0) & I(1), then go for ARDL model. it will be showing both long run and short run relations.
I think these information will be helpful for you.
The linear regression itself, it is just an adjective not a technique, I think you wish to adopt OLS technique with varibles more than two series. There are rules guiding this technique, which had been well explained by Neog above. Hope you are satisfy with that.
