To answer to criticism of spurious regression, if it is time trended. Causality is still a bigger issue than just uncovering stationarity of time dated series. We need the theory to guide us and the use of statistics in experimental research design to handle causality is still not resolve.

• Stationarity in economic time series is not only an econometric issue but rather a serious problem that has important consequences for the significant interpretation of the model.
• Evaluating the properties of the data before estimation helps in avoiding the so-called spurious estimation.
• Taking the first difference or higher may lead to the loss of long-run information.

Thank you, dear Manhal Shotar

1) If you do not make your data stationary then spurious correlation can be a problem.

2) Taking logs will not make series stationary, but it will help make modelling assumptions more plausible.

So taking logs and diffs should be done together, if necessary. But instead of taking diffs you can use alternative approaches, see this discussion: https://www.researchgate.net/post/What_methods_instead_of_taking_differences_would_be_remedies_to_non-stationary_variables

Dear Andrey Davydenko thank you very much. I will also read the discussion that you recommended.

Hi

Stationarity of variables is very key in estimation as one is likely to obtain unreliable results if not ascertained before any analysis.

Ibrahim,

I think you must use time series data stationary of the same order to run your regression(s). If the dependent variable is stationary then your independent variables should also be stationary, otherwise your regression results cannot be trusted. As for taking the logs this is fine but you need to do unit root tests for these variables as well . Again all your variables in the regression have to be stationary of the same order. You can mix the variables in the regression some in logs and some not. There are several unit roots in addition to ADF test and you should learn and use them there are advantages. So I think you should look in the theory to find other variables that will allow you to run the regressions without violating basic principles of time series econometric analysis regarding the dynamic properties of the stability properties of the time series variables.

best luck

George K Zestos

Dear Ibrah,

It depends a lot on what you want to do. If you want a univariate analysis, then making the series stationary makes a lot of sense. These univariate analyzes work because Yt and Yt-1 follow the same trends. Of course, you need to check for a deterministic trends in such analyzes. However, if you need to work with multivariate analysis (var, vec or regression) then you need to check if the variables are cointegrated. When there is cointegration, working with the first differences will create bias by omitting relevant variables associated with error correction terms. For example: if Y and X are co-integrated you can work with Yt = a + bYt-1 + cXt + dXt-1 + Ut or DYt = a'DXt + c '(ECt-1) + Ut, where EC is the error correction term and DYt = Yt - Yt-1. Today, every econometrics textbook explains the error correction term and the relationship of these 2 models. See, for example, the paper of Hendry and Juselius - explaining cointegration analysis part 1 and 2 or any econometrics textbook.

Yes of course it is a crucial test

While it is important to ensure the stationarity (through differencing) of time series data prior to the model estimation in order to avoid the problem of spurious, it is also important to note that the difference approach to stationarity usually leads to the loss of important long-run information. Thus, the need for cointegration test. If cointegration is found among some sets of similar non-stationary time series, then regression can proceed without generating spurious results. The implication of cointegration is that any deviation from equilibrium is considered to be temporary as equilibrium holds in the long-run. Therefore, when variables are non-stationary but are cointegrated, the level equation is normalized and interpreted as long-run coefficients, while the difference of the variables are modelled alongside the a period lag of the error term from the level equation to serve as the error correction term in an error correction model. The reason for the error correction model is to reconcile the long-run behaviour of variables with their short-run responses as well as to scientifically validate the convergence process on the path of long-run equilibrium. Thanks.

Logs do not make time series stationary, but, in general, logged variables are very near to stationarity. The problem is that they reduce all fluctuations, therefore avoiding to (clearly) see patterns. This likely leads to spurious results. I think, you should put much more effort in a careful specification of your model and in a thorogh analysis of your data and their relations. If you have found satisfyingly specified equations (by which I mean functions, transformations and hypotheses on the margins, within the coefficients should be), I recommend to take the differences (absolute differences for linear and dln or %-changes for exponential functions) for the estimation, because this is a much "sharper" test. Not be disappointed, if estimations show "bad" statistical results. A proof against your hypotheses may be of a scientific value, too.

As many have pointed out, if the explanatory variables are non-stationary, in an OLS regression, you will most likely get spurious results, i.e., what you are picking up is only the trend in the variables and the variables may not have any meaningful relationship. Another thing that I find curious is that you mentioned that the dependent variables are stationary but the log of the explanatory variables are non-stationary? I'm not sure that this makes sense both statistically and economically. Perhaps a rethinking of the model may be in order?

Dear Ibrahim.

It is always the best idea to have stationary data. This helps to avoid spurious regressions and unreliable results.

It also makes your assumption more plausible.

In addition, it is best for all your variables (dependent and independent) to be stationary at the same level. That gives you confidence concerning your end results.

Regards

Thank you for all your valuable and interesting answers Kehinde Mary Bello Francis W Ahking Anton Rainer Chekwube Madichie Mohamed Ait El Fakih Leonardo Oliveira George K. Zestos Samuel Tawiah Baidoo

Yes. You have to check the stationarity of the variables. Always remember, an application of every test in time series depends on integration order of series or variable. If your DV is I(0) and log of IDVs are I(0), there is no problem you can apply OLS regression on these I(0).

you can try many tests e.g second difference, you can try to difference dependent variable separate, you can try second difference of the independent variables separately

Dear Miklesh Yadav and Philip Kilonzi , thank you very much!

Dear Ibrahim.

Yes. It is a research in which you can carry out a lots of tests to verify your results.

You can go ahead with the second difference and compare the results with the first difference and then verify which one gives you a more reliable result.

Regards

To answer to criticism of spurious regression, if it is time trended. Causality is still a bigger issue than just uncovering stationarity of time dated series. We need the theory to guide us and the use of statistics in experimental research design to handle causality is still not resolve.

very ideal to have stationery data

Dear Ibrahim,

You have to work with stationary series in time series analysis.

Otherwise, the spurious regression problem occurs. In addition, it is very important to determine the trend-stationary or difference-stationary process of the series correctly in the stationarization process.

In the trend-stationary process, the difference of the series is not taken. Actually, this is the most important part. Generally, the mistake made is, the stationary approach that by take the difference of all series. If you are careful about this, you will not have any problems.