Lag selection for Augmented Dickey Fuller test

Apologies in advance, I am a beginner so these questions might be quite simple. I am testing log real exchange rates for unit root stationarity for EU15 countries. I was wondering what is the best way to select the optimal lag length if I have 100 observations.

I've got three questions:

1. I was using the AIC and SIC to determine which is the best fit, but at the same time I don't want to have too few lagged differences. Where do I find the balance? What's the best approach?
2. What do I do when AIC and BIC are negative? Choose the more negative one?
3. For Greece for example, I can see a decline i.e. a time trend, but when I add it, it turns out to be insignificant, what's that about?

Thank you in advance for any help!

• AIC/SIC are there to make sure that you have a balance beteween too many and too few. There are many criteria around in active use, so it is kind of to be expected that there is not a single "best" one that is to be preferred all the time. Hence, we have to live with the fact that there may be disagreement among different lag-length selection criteria. And yes, always choose the smallest value, so -50 is better than -40. Apr 23, 2015 at 14:51
• I am no expert in exchange rate modelling but I would think twice before include a trend in the ADF test regression. If you had a model to explain why the trend was there, it could make sense to account for it; on the other hand, a "trend" in something as "random-walkish" as currency exchange rates may be just a coincidence (a random walk can have patterns that look somewhat like pieces of linear trends). Apr 23, 2015 at 17:37

The first question has been discussed extensively in the literature. Some propose using the AIC or SIC criteria, others employ significance tests. To cite just a couple of references, Ng and Perron (1995) compared methods based on information criteria with sequential testing of additional lags. Ng and Perron (2001) propose a modified information criterion.

I agree with @ChristophHanck that there isn't a single strategy that will perform better than others in any possible situation. The residuals of the Dickey-Fuller regression should be inspected instead of trusting the choice of a given procedure. If serial correlation remains in the residuals, then one additional lag can be added until no structure is detected in the residuals.

Bootstrap is an interesting alternative because it can potentially deal with any kind of autocorrelation beyond those structures explored by simulations in the literature.

Note: P-values based on the original critical values may be a rough value. The distribution of the statistic has been tabulated for some fixed sample sizes and do not account for serial correlation. Cheung and Lai (1995) employed the method described in MacKinnon (1996) based on response surface regressions to obtain a procedure that gives the p-value of the ADF test for different sample sizes and lag order selection methods.

References

Cheung, Y. and Lai, K.S. (1995) Lag Order and Critical Values of the Augmented Dickey-Fuller Test. Journal of Business & Economic Statistics, Vol. 13, No. 3 (Jul., 1995), pp. 277-280. URL

MacKinnon, J.G. (1996) Numerical Distribution Functions for Unit Root and Cointegration Tests. Journal of Applied Econometrics, Vol. 11, No. 6 (Nov. - Dec., 1996), pp. 601-618. URL

Ng, S. and Perron, P. (1995) Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag. Journal of the American Statistical Association, 90(429), 268-281. DOI

Ng, S. and Perron, P. (2001). Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power. Econometrica, Volume 69, Issue 6, pp. 1519-1554. DOI

• Thank you for your answer! I was just wondering: if I want to increase lag-length to eliminate autocorrelation, but the lags are completely insignificant, how do I find a balance? Apr 24, 2015 at 19:10
• If there is autocorrelation but the lags that you add turn out to be insignificant, it may be that the autocorrelation happens at higher orders. You could try removing the insignificant lags and checking whether higher order lags are significant. Apr 24, 2015 at 20:52
• How many times can I difference it before it becomes unreasonable? Apr 24, 2015 at 21:28
• There is no rule, it depends on the data. Overdifferencing induces negative correlation, see for example this post. If consecutive negative autocorrelations show up in the partial autocorrelations, this may be a sign of overdifferencing. Apr 26, 2015 at 10:15