Try to plot the graph for each variable to see if there's a marked shift in the level or the variable is entirely trendy, with this you would know if your variable requires a constant and trend or otherwise. In the same vein, you assume the variable has constant and trend and check the unit root, if that isn't significant then u go for constant only. The option without constant or trend is usually meant for transformed variables like differences variable. Another way is to try to estimate a simple Ols including the constant and trend to see if either the trend, constant or both are significant. For example. GDP = c + @trend

If the constant is significant and trend isn't, try constant only, if both are significant try constant and trend

Best Regards

Humid Muili, Follow your answer

As a practitioner, I am sympathetic with the advice to "try all possible options to be on the safe side for unit root tests". However, if you obtain contradictory results, then you need to think theoretically about the time series being modelled. The ADF (etc.) with no constant (drift term) and no deterministic time trend is testing for a pure random walk (i.e. a model in which the variable is purely stochastic and can thus go anywhere, in which case the best predictor of the future value is the current value). Some variables, e.g. currency values, are like this. However, real economic variables are not purely stochastic but also respond to fundamentals. In this case, a random walk with drift is an appropriate univariate model: the drift term captures the deterministic impact of economic fundamentals (giving the variable a tendency to move up or down in every period); while the unit root captures the stochastic component (which may either reinforce or offset the deterministic drift term in any given period). Philosophically, this is appealing: we live in a universe that is neither completely deterministic nor completely random. Finally, it is possible that the stochastic component of the evolution of a variable may unfold around not only a drift term but also a deterministic time trend. So test for this as well. In conclusion, these possibilities should be considered in advance of running tests. And in all cases, look at the graph of the variable to be tested!

I would agree with Geoffrey Thomas Pugh. If I provide an answer, it is only to suggest a redesign of your plot. First it is practically impossible to distinguish the curves. Second, there are two groups of series that should be shown on different scales. That would help you to decide in favour of constant plus trend, I suppose. Be careful that you have many tests and few observations (I think).

The ADF test for the necessary condition of cointegration involves testing each individual variable for its order of integration (the advice on deterministic terms given by the answers of others above may be followed). If the variables have the same order of integration (typically I(1)) the necessary condition is satisfied. The EG-ADF test for the sufficient condition of cointegration involves testing the residuals of the potential cointegrating equation whether it is I(1) or I(0). Be cause this potential cointegrating equation should include an intercept (and possibly a trend) its residuals will have a zero mean. Hence, to obtain a correctly sized test, the EG-ADF test on the residuals of this potential cointegrating equation should NOT include either an intercept or a trend.

In an ADF style unit root test the null hypothesis is that the time series being examined is non-stationary. The choice of

to be used in the test depends on the alternative hypothesis that you consider appropriate

If you use the wrong alternative, at best, you will lose efficiency and possibly your results will not be valid. I would also say that 20 observations are, almost certainly, not enough data for these tests. If you do get enough data I would also recommend that you use the DF-GLS version of these tests as they generally make better use of your data,

time seriestime seriesThe lag length to be used is often based on an information criterion (AIC or SIC). The optimum lag length is found by testing down from a maximum lag length of

integer part of 12 * (T/100) ^(0.25)

For a sample of 75, this is 11.

The application of the Engle-Granger test is more complicated. The critical values depend on the number of regressors and on whether the regressors have drift or not. They are different from those used in the ADF test. An appropriate lag length is usually based on a method similar to that used in the ADF type unit root tests. For details, you should consult a book such as the Enders time-series textbook.

If you have cointegration you automatically have Granger Causality. Testing for Granger Causality in the presence of non-stationary variables is non-standard.

With 20 years of observations and 6 countries, I would be thinking more of some form of stacked OLS or SUR estimation or something in between. Are you missing any important variables in your economic model. (missing variables will lead to biased estimates of your coefficients.

Dear Maximilian.

Try the graphical approach first to see the trend and movement of your variables.

Then carry out unit root test to test if the variables are significant.

Then as regards Granger Causality, be mindful of the lag length you selected for a good result.

Regards

Thank you very much for all these helpful explanations Kehinde Mary Bello John C Frain Chris Stewart Guy Mélard Geoffrey Thomas Pugh Fethiye Burcu Türkmen - Ceylan Hamid Muili

I'm sure they did not only help me but everyone trying to get a better understanding of this!

Maximilian: There are several good suggestions given here for testing for stationarity/non-stationarity using the augmented ADF tests. No one has offered to answer the question concerning constant/deterministic terms in cointegration equations, which is a more important question. I have published a paper 30 years ago which addressed exactly this questions and other issues, you may find it useful to take a look at the paper: "Model mis-specification and Johansen’s

co-integration analysis: an application to the US money demand", Journal of Macroeconomics 24 (2002) 51–66. I don't know whether there has been additional research on this question since my paper. The main takeaways from my paper are:

1. There is very little in the literature that would allow you to determine whether constant/deterministic terms are part of the cointegration equations

2. In my case of U.S. money demand, I got very different results when constant/deterministic terms are included or omitted from the cointegration space

See if my paper may answer some of your questions. Good luck with your research.

Good day

Kindly find the attached article, I believe it will help you. We've applied the ARDL model.

Kind regards

Nkoti Solly Molepo

Nkoti Solly Molepo Thanks a lot!

Nkoti Solly Molepo I have read your paper. There are many facets to it that I feel might mislead someone, seeking advice on this type of model. I have attached a pdf file that explains my points in more detail.