I am investigating the order of integration for a particular variable of my analysis: yearly deforestation rates at state level. First, it must be said that data about this variable has been interpolated in order to obtain a time-series: interpolation of forest cover data from different year (approximately each 5/10 years). It is a common procedure – although highly questionable – for this variable, even data provided by FAO are interpolated. Note, I employed a cubic spline interpolation for my data while FAO relies on a simple linear interpolation between “dots” over time. This variable of interest span from 25 up to 51 years (it depends on the specific state and on data availability).
However, going to my question. When I perform unit root test for my panel (both for the whole dataset, approximately 100 countries but also for sub clusters, e.g. regions such as Latin America etc.) I commonly obtain mixed I(0) and I(1) results. I performed both first- and second-generation panel unit root test (es. LLC, IPS, CIPS, and CADF). However, when I performed unit root tests for each country (es. ADF, PP, DF-GLS, and KPSS) my results lead me to conclude that those variables are I(2) – sometimes even I(3)! Nevertheless, those results for the specific country time-series does not concern me too much (yes, I would have preferred to have I(1) variables instead) since the scatter plot show really shoot curves and those are commonly with an I(2) order of integration.
My question is the following. In which test – and thus result – I should rely the most?
N.B. When I perform country-specific unit root tests using data obtained through a linear interpolation (the one provided by FAO) results basically conclude for I(1).
I think the core issue may be that you are applying unit root tests to interpolated data. Put simply, these tests are looking at the first order autocorrelation in the data but in your case such autocorrelation is largely the result of the interpolation method and carries little information about the data generation process. With your actual observations being 5/10 years apart, I think it's going to be difficult to examine the nature of any first order autocorrelation.
As to the results from the FAO data, this may be an example of the general principle that if the trend term in your test (here, I presume, simple linear) differs from the trend process in the data (here, piecewise linear) then tests will often account for that difference by mistakenly concluding I(1).
We cannot say that it is your interpolation that created your problem. Assume that you that pretesting are unimportant, then apply ARDL technique. Also, you may run your data on tests that do not assume mixed integration. By comparing the two you, it gets clearer.
An interpolated series is probably smoother than would be the case if no observations were missing. This tends to produce a higher estimated AR1 coefficient and thus more likelihood of a test concluding "unit root". (I have confirmed this with a small Mont Carlo experiment)
Thank you Chuck and Vince for your answer. I personally agree with Vince in saying that the interpolation methodology could play a "big role" in determining my results. However, I will try to carry out some country-specif test and regression as suggested by Chuck but I am a bit skeptical about some possible interesting results.
I checked again my data to a panel level analysis. This time I added a different lag-order, from 3 to 4 (selected by the command varsoc conducted for each time series) and results are - obviously - more in line with those of the country-specific unit root test. For sure I should have checked before the proper lag-order (even before posting this question). However, in my experience I encountered very few papers which have showed some information about the lag order selected. In fact, the lag order identified by the common commands lags(aic) and lags(bic) usually conclude for 1 lags.
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