AIC is the best

AIC

AIC is a bit lenient in terms of lag selection compared to SIC. hence, if you want a short lag selection perhaps if you are having a short time series. You can go for SIC. although, in lag selection using these criterion, the software different criterion selection statistic can concur on a particular lag. So if this is the case, you can go for the lag agreed upon by these criterion. Although, these criterion selection statistic only give an optimal lag selection, you can go for a lower lag if the length of your time is not too long.

Best regards

Try to use AIC Criteria, however in some cases SIC can also be helpful.

Whichever criterion you choose the residuals in your equation must not be serially correlated. If the residuals are serially correlated your estimated coefficients are not consistent. This applies whether all your variables are stationary and you are estimating a stationary dynamic ARDL model or if your variables are a mixture of I(0) and I(1) variables and you are completing an ARDL bounds test.

I would look at the results using all criteria. As the SIC gives the most parsimonious model I would look for autocorrelation in the estimated residuals. If there was no autocorrelation I would use the model based on SIC. Otherwise, I would look at the less parsimonious models. To me, these criteria are a starting point in the choice of lag length.

(You might also note that ARDL estimation requires that exogeneity conditions be satisified)

AIC is better than others

Remember AIC is a bit lenient while SIC is a bit strict

@ Gbenga Adeyemi, thanks for your time & contributions.

@Hamid Muili, thanks 🙏 very much for further information on the selection criteria. Blessings!

@Imran Khan, thanks for your short & significant answer.

@ John C Frain, thanks for your comprehensive explanation on the selection criteria. I also encountered a situation whereby ADF reported say all series to be I(1) & two other unit root tests reported same series to be purely l(0)s. In that case, can we agree that all series are truly I(0)s? Secondly, can we apply ARDL (p,q) model to analyze such series?

Model persimony should be considered. Hence use SIC.

@Saheed Busayo Akanni. My earlier reply got a little confused somehow and I will try again. I am using an android tablet and it may have problems with ResearchGate.

I do not have enough information to answer your question. The following are some points that you might consider.

1. The DF-GLS version of the ADF test is generally regarded as best.

2. Does economic theory/common sense indicate anything about unit roots in your variables? How have they been used in other studies?

3. By what margin did the second unit root tests fail the null of a unit root?

4. The ARDL can be used in many circumstances. Two common used are (a) As a dynamic regression model when all the variables are stationary and (b) Pesaran's Bounds tests and estimated countegrating relationship. Pesaran''s book "Time Series and Panel data econometrics" contains an account of this theory.

5. Is your sample large enough to support this analysis?

you can choose the lag length criteria based on your data not methodology that you use. For instance, Liew (2004) argued that the AIC is better than the HQIC and BIC monthly data.

Pesaran and Shin (1998) argued that the BIC criterion is appropriate for annual data and is slightly better than the AIC with a small sample size.