logging variables does not remove unit root from a series, it only smoothens the line a bit and make interpretation easier as it will be interpreted in percentages.

Reporting either ADF or PP is at your own discretion. But for confirmatory purpose you can report both ADF and PP unit root test as well as KPSS stationarity test provided your variable does not have a structural breaks.

Furthermore, Using 11 variables might be too much except you have a very large dataset say 100 or more. Because using a large variables on s sample size shrinkens the degree of freedom which might affect the true inference made from the estimation

Best Regards

logging variables does not remove unit root from a series, it only smoothens the line a bit and make interpretation easier as it will be interpreted in percentages.

Reporting either ADF or PP is at your own discretion. But for confirmatory purpose you can report both ADF and PP unit root test as well as KPSS stationarity test provided your variable does not have a structural breaks.

Furthermore, Using 11 variables might be too much except you have a very large dataset say 100 or more. Because using a large variables on s sample size shrinkens the degree of freedom which might affect the true inference made from the estimation

Best Regards

If I understand your question correctly that you want to use data in log form in your model:

• Then you need to test for unit roots in log form as well.
• Before that, and as a first step, I recommend that you visually inspect and check the data.
• Reporting both tests' results, while explaining the subtle differences between them, is the better choice.
• Finally I agree with Mr. Hamid Muili regarding your last point that smoothing the data is different from removing the unit root.

Thank you, dear Hamid Muili

Great thanks dear, Manhal Shotar

Log transformations typically stabilize the variances of the underlying series. With regards to making a choice of using either ADF or PP or both, please consider the size of your sample. The ADF performs well even when the sample size is fairly small (Dickey & Fuller, 1979 ), while the PP criterion non-parametric approach which does not require selection of the level of serial correlation as in the case of the ADF, but corrects the statistic for autocorrelations and heteroscedasticity.

The PP approach is based on the asymptotic theory, hence it works well largely, if not ONLY, on large samples. Nonetheless, it usually advisable in practice to run several tests (ADF, PP, etc) for comparative purposes to assess time-series properties - eg structural breaks, etc. Consider reading - Dickey, D. A., & Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74, 437- 431.

All the best!

yes

To check unit root of series in this case,we can use ADF test of unit root.

Yes. You still need the ADF and/or PP unit root test even with logged variables.

DF measures if the mean of a series is stationary, if it is not, the first difference is used to transform it into stationary. The logs help to correct the stationary in variance

Dear Ibrahim

In some cases, the use of logY can reduce the heterogeneity of the original series Y and improve the performance of ADF tests. Both cases (logY or Y), you need to check the stationary and cointegration of the series.

Thank you, dear Leonardo Oliveira

Thank you dear Mariano Méndez-Suárez Emmanuel Ikpe Michael Anant Srivastav Elvis Munyaradzi Ganyaupfu

log transformation help us reduce the heteroscedasticity problem which may be found on data, but it is not necessary that it will remove the unit root problem. hence it is essential to do unit root test if we are going through time series analysis

Thank you, dear Amritkant Mishra

yes, you need it to check the stationarity of data. if data is logged it doesn't mean it is stationary. you can use both ADF & PP or either one

great thanks Abdullahi Osman Ali

Yes, you still need the ADF.

It seems that this question and the question you posed on the following day ("Is making the data stationary is always a good decision?") are connected. Therefore, I assume you want to estimate one equation where the dependent variable is stationary and the 11 explaining variables are not. Under theses conditions, it is highly unlikely to find a good specification. But without a well specified model, you cannot get reasonable results, even if you use the best available econometric procedures. Many (most?) econometricians underestimate the importance of model specification and do not put much effort in it. In fact, I think, that specification is more important than statistic estimation. One hint for this underestimation is, that they simply change to logs (if the estimation in absolute values is unsatisfying) without recognising, that this transformation means a change of the model.

yep if you do the distributed lag regression model; for example: BA = a+ b t + ct-1 (t= time; one year)

Yes, you need to check and report the unit root test(s) if it is a pre-condition for utilizing your choice of technique.

Lastly, transforming a variable into its log form does not make it stationary.

Yes, you still need to test for stationarity even if your variables are in log form. Log transformation does not remove unit root.

Log transformation does not eliminate unit root. You should confirm this by making a visual plot of both logged and unlogged series. Also, you should be able to know from the visual plot which series exhibits stationary or non-stationary movement.

There is some misunderstanding here.

If a variable is non-stationary then a transformed version of that variable is non-stationary. Thus if y is nonstationary then log(y) is non-stationary. Log transforming a non-stationary variable can not make it stationary.

Sometimes the first difference of a non-stationary variable is stationary. Such variables are said to be integrated of order 1 denoted I(1).

For example, a time series of real GDP is often found to be non-stationary. The log of GDP is also non-stationary. The first difference of the log of GDP is often found to be stationary and therefore log(GDP) is I(1). GDP is non-stationary and is not I(1) (and is probably not integrated of any order).

If a variable is stationary then a transformed version of that variable is also stationary.

The use of transformed variables in econometrics is best indicated by theory. If shocks have a multiplicative effect use logs. If they have an additive effect then use untransformed variables. Does your model predict marginal effects, or elasticities, or semi-elasticities etc.

As usual, John's comment is correct, but may I add, that relations between explaining and dependent variables may be indirect (via other variables, possibly with no or few data) and more complicated than only additive or multiplicative. Therefore, it is very important to carefully specify a model and to analyse the data. From this specification, one can derive the feasible transformations (including - if possible - approximative linearisations of the functions) of the variables.

Anton Rainer I could not agree more.

Variables in their log forms can still have unit root so yes, you to perform the ADF test to avoid spurious regression results.

Dear colleagues, I learned so many new things from your answers, thank you very much. Prince Fosu John C Frain Anton Rainer Chekwube Madichie Sheunesu Zhou Sara Onur Johnson Oliyide Jones Odei-Mensah

it does not mean. you can still use it.

I do not understand, why one should apply an ADF-test in this case. If (most of) the variables are non-stationary, their logs will, in principle, non-stationary, too. That is logical, and no test is necessary to show that. The point is, that regressions with such data are likely to give spurious results, which cannot be avoided by stationarity tests. I think that this is what Judith meant with her answer: These data - even in logs - cannot be used for a reliable regression.

Yes, you can use the log-transformed data to check the stationarity of the variables through ADF or PP unit root tests.

Dear Ibrahim Niftiyev , I endorse the explanations by John C Frain . Generally, data transformations will not turn your stationary series into non-stationary and vice versa. Furthermore, of course you need to test the stationary property of your series. Additionally, it depends on your situation whether you need to report your unit root results; nevertheless, you need to investigate the primary step of unit root testing for your time series before you go for further analysis. Apart from all of this debate, it would be advisable to always test the unit root property of the time series before entering the main analysis for generating inferences.

Log transformation makes the distribution of a series symmetrical, and not stationary as already elaborated extensively by John C Frain