DATA SERIES CHECKING: Check you data series to see whether you have I(0) and I(1). The two tests: Johansen and ARDL cointegration tests are not used intergeably.

JOHANSEN TEST: This is used for testing cointegration of several I(1) time series. If you have several time series that are integrated as I(1), then using the Johansen test is appropriate. This test is generally used in vector auregressive model VAR(p) where VAR(p) is given by:

Yt = C + A1Yt-1 + A2Yt-2 + ... + ApYt-p + et

... C = k X 1 vector of constants (intercepts); Ai = time invariant k X k matrix and et = k X 1 vector error.

ARDL COINTEGRATION TEST: Under this approach, the test incorporate I(0) and I(1) in the same estimate. If the variables are I(0) only then use OLS. it is easier and simpler. If the variables are I(1) only then do VECM (Johansen test). If the variables are a mixed of I(0) and I(1) then use ARDL test.

Check your time series to see whether you have a mixed of I(0) and I(1) or either one without the other---if so, follow above suggestions.

REFERENCES:

(1) Johansen, Søren (1991). "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models". Econometrica 59 (6): 1551–1580. JSTOR 2938278.

(2) Hatemi-J, A. (2004). "Multivariate tests for autocorrelation in the stable and unstable VAR models". Economic Modelling 21 (4): 661–683. doi:10.1016/j.econmod.2003.09.005.

https://nomanarshed.wordpress.com/2014/11/16/a-manual-for-ardl-approach-to-cointegration/

Thanks Paul, it is clear.

Two published papers below may provide practical example:

ARDL COINTEGRATION TEST

https://www.researchgate.net/publication/233000913_Capital_mobility_in_Asia_evidence_from_bounds_testing_of_cointegration_between_savings_and_investment

JOHANSEN TEST

https://www.researchgate.net/publication/266456827_COINTEGRATION_AND_CAUSALITY_BETWEEN_STOCK_INDEX_AND_MACROECONOMIC_VARIABLES_IN_AN_EMERGING_MARKET

Article Capital Mobility in Asia: Evidence from Bounds Testing of Co...

Article COINTEGRATION AND CAUSALITY BETWEEN STOCK INDEX AND MACROECO...

Microfit software can give the best result for ARDL. Eviews can give the best result for Johansen test.

Please Monir Ahmed, what of the Stata software? Thanks

i run both cointegration test for the same data in which all the variable are integrated of order. Johanson results shows that there is no cointegration but ARDL shows there is.

which one is true ?

any reference for this

J cointegration OLS we use at level I( O)

But for ARDL used when I(1) and I (0) together

if variables are cointegrated we run restricted VAR (VECM)

but if the variables are not cointegrated we cannot run VECM but we use unrestricted VAR