I read that the validity of unit root test becomes very small if the number of observations is small. In this case, it is very likely to have Type II error, say wrongly accepting the null hypothesis of unit root.
So for a very short time series, t=21, is it necessary to do unit root test?
Thank you very much!
Small samples does not require unit root testing.
You are also likely to have size distortions (i, e. the confidence limits are not correct for such a small sample). You may have to depend on theory to determine id your series has a unit root.
Even if you do come to some conclusion about the series being I(0) or I(1) you are likely to have problems deriving any decent results, even if your series is I(0). One can not be certain about this until you try. A little more information about the nature of your data and your research topic might be useful. If you have a model in mind how many coefficients are you trying to estimate with 21 observations
Dear John,
Thank you very much! The 21 observations are used to estimate the trend in terms of trade by a trend equation, y=a+bt, where y is log terms of trade, t is the time variabe, and b is the trend rate. So there is only one coefficient to be estimated. Such a small sample size is definitely poor, but it is basically impossible to expand the size.
Some previous studies used sample size of less than 20 to do the same kind of analysis, and they did not mention anything about trend stationarity. However, some other studies on long-term terms of trade, like 80 years, discuss and test trend stationarity.
My first reaction would be to suspect that the terms of trade are non-stationary. After all some change of supplier of some import is likely to have a permanent effect on import prices. Some technological innovation at home may have a permanent effect on export prices. If you decide that the terms of trade are I(1) then the appropriate estimator of b is the average of the first differences. If you decide that it is I(0) then use standard regression. Possibly both estimates are very similar. Have a look at a graph of both lines and the data.
Dear John,
Thank you very much once more! Just one more question. For correcting for the first order autocorrelation in time series data, there may be several methods, like Newey-West estimation, Prais-Winsten/Cochrane-Orcutt FGLS estimation, and maximum likelihood. It seems that Newey-West estimation may not be widely used. So how to make a choice between maximum-likelihood and W-P/C-O estimation?
It is difficult to deal with auto-correlation when the sample is small. Results are generally asymptotic and do require large samples. Is there a possibility that the auto-correlation is caused by an outlier. If you add a dummy for that observation does the auto-correlation vanish.
If you have a particular model in mind can you give sensible values to the parameters, simulate the model, and see if you can extract the original values.
Incidentally I would expect that the last four estimators would give similar results. If this is the case there is no need to make a choice,
Auto-correlation tests are often regarded as specification tests.
Many thanks again. In the terms of trade literature, some authors use maximum-likelihood to correct for autocorrelation for small sample size, while some (but perhaps less) use GLS. But my general impression is that their treatment on autocorrelation under small sample is relatively rough.
Btw, I am not sure about the advantage of Prais-Winsten estimation over Cochrane-Orcutt estimation. Some argue that for small sample P-W is better because it keeps the first observation. But is there any other advantage of P-W over C-O?
There is no need because variables re relatively stationary in the short term.
I think the unit root tests for panel data with time series less than 10 is not required.
Is there any reference/study you could share about not requiring unit root testing for small samples?
- Badges
- Science topic