While cointegration tests are often used to assess the long-run relationship between variables, they are not always necessary, especially if you are primarily interested in short-term dynamics or if your variables are already stationary in some form.

If your variables are stationary after differencing, it suggests that they may exhibit a relationship in changes or first differences. In such cases, you can go ahead with your analysis using the variables in their different form.

However, if you suspect that there might be a long-term relationship between your variables even though they are stationary in differences, then conducting a cointegration test could be beneficial. Cointegration tests help determine whether a common stochastic trend exists among the variables, indicating a long-run equilibrium relationship. This is particularly relevant if you want to understand how the variables move together over time.

In summary, while cointegration tests are not always necessary, they can provide valuable insights into the long-term relationships between variables, especially if you suspect such relationships exist despite the variables being stationary in differences. Ultimately, the decision to conduct a cointegration test should be based on your specific research questions and the characteristics of your data.

Cointegration focuses on whether there is a long-run relationship between time series variables or not.

If the variables have an order of integration of I(0) and I(1). The appropriate cointegration test is the Bound test.

The cointegration analysis was done by estimating Engle-Granger co-integration as the residual-based approach.

If the residuals contain a unit root, then there is no cointegration (the residual is stationary in levels implies that there is cointegration among the variables).

Then, after testing cointegration exist b/n variables an error correction (EC) model can be estimated.

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