When the variables are integrated in different orders then you should run the ARDL bound test rather than any cointegration test.

Your variables must be integreted of either I(1) or I(0).

If you have a mixed order of co-integration, it is preferable to utilize the ARDL approach for estimating short-run and long-run coefficients of your proposed econometric model.

With a sample size of 21 the ADF test has very small power and should not be used. I would also doubt the validity of any cointegration analysis with this sample size.

Use ARDL Provided none of the variables is integrated of order two I(2).

This simple thing to do is to use Autoregressive distributed lag(ARDL) but your sample size is disturbing (too small)

When variables are integrated in different orders (e.g., one variable is I(1) and another is I(0)), the appropriate cointegration approach to use is the **Johansen cointegration test**. This method allows for the analysis of cointegration relationships between variables that may have different orders of integration. It determines the number of cointegrating relationships and estimates the long-run equilibrium relationships among the variables.

When variables are integrated in different orders (e.g., some are integrated of order 1, I(1), and others are integrated of order 0, I(0)), the appropriate cointegration approach to use is the ARDL (Autoregressive Distributed Lag) model.

ARDL models can accommodate variables with different orders of integration by including both level and first-difference terms in the regression equation. This approach allows for testing cointegration among variables with mixed integration orders and provides robust results under various scenarios.

In summary, ARDL models are suitable when you have a mix of integrated and non-integrated variables and want to test for cointegration relationships among them.

When dealing with variables integrated at different orders, you should use the autoregressive distributed lag (ARDL) approach to cointegration. The ARDL model can handle variables that are integrated of different orders (I(0) and I(1)) and is particularly useful when the integration order is not uniform across variables.

Use the autoregessive distributed lag (ARDL) approach. It can handle variables integrated at different orders, including I(0) and I(1).

When variables are integrated of different orders, use the Autoregressive Distributed Lag (ARDL) approach for cointegration. The ARDL method allows for different integration orders (e.g., I(0) and I(1)) and can be used to test for long-run relationships and short-term dynamics.

when that scenario occurs, use the Bound test ARDL cointegration approach which accommodate varying orders of cointegration.