The information criteria for optimal lag length  is contingent on the number of observations. While the AIC and Final Prediction Error (FPE) are more appropriate when observations are less than 60, the Hannan-Quin is more efficient when observations are above 120. Moreover, it remains the discretion of the researcher to select the maximum lags  which the adopted criterion for choosing optimal lags will use.

Reference

Liew, V, K-S., (2004). "What lag selection criteria should we employ?", Economics Bulletin, 33(3), pp. 1-9.

Thank you for your comments and reference.

I think the question is not yet settled.

I'm not sure that it remains the discretion of the researcher to select the maximum lag  which the adopted criterion for choosing optimal lag will use...

I find that the proposed exercise in Liew paper  is interesting, but not enough ...  

Information criteria are the initial measures that can be aopted when selecting the appropriate 'lag length' in a time series. However, we can get conflicting conclusions regarding the 'lag length' when these criteria are used. Let me calrify using the example of estimating a VAR model. Firstly, one should use sufficiently large number of lags when estimating a VAR model, ofcourse depending on the number of observations. Secondly, he should test if the same model can be estimated with fewer lags on the variables included. Thirdly, he can test the cross equation restriction using the 'Likelyhood ratio' test. If the LR test decision goes in favor of a more restrcited model, we should estimate the VAR model using fewer lags. Hence appropriate lag lengths can be chosen by paring down the 'lag length' using the 'likelyhood ratio' test, especially when the sample size is not small.  

In general, we use all criteria cited above and after that we take the smallest lag length from them.

My favorite publication on this topic is still the book by McQuarrie and Tsai "Regression and Time Series Model Selection" that contains numerous simulations. They find no generally "best" criterion (and it does not exist as it depends on what we want to optimize) but it is obvious that the standard AIC yields too many lags in small samples. The corrected versions AICu and AICc perform slightly better.

Thank you for your comments and reference.

I think that the debate is still open...

you can refer to

http://www.fucape.br/_public/producao_cientifica/2/Carrasco%20-%20Selection%20of%20optimal.pdf

Dear Jamal,

Another useful argument is presented in Hendry and Juselius (2001) in the context of Johansen cointegration. They suggest that the lag length ought to be set such that the VAR residuals are free of autocorrelation, even if this implies longer lags than suggested by the information criteria.

Best,

Oana Peia

Hendry, D. F. and Juselius, K. (2001), `Explaining Cointegration Analysis: Part II', Energy Journal 22(1), 75.

You can consider AIC or Schawart value to define it. 

First, thank you for pointing out the problem of lag-length selection. Generally, applying a statistical technique as information criteria (AIC and BIC) to select lag length is probably less parsimonious than carrying out sound econometric judgment. This does not mean that these criteria are not sufficient in several cases. Various studies already indicate that Akaike criterion is preferable… However, in computational framework, Serena and Perron (2001) proposed a modified information criteria (MAIC and MBIC) by accounting for the severity of size distortions and power loss, using local asymptotic properties. In their research, they compared the values of the proportionality factor of AIC and MAIC on the one hand, and BIC and MBIC on the other hand. Briefly, they highlight the great usefulness of MAIC compared to the rest of criteria. But this assertion, of course, needs further assessments (i.e., awaits confirmation)…

Reference:

Serena Ng and Pierre Perron (2001), “Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power.” Econometrica, Vol. 69, No. 6, pp. 1519-1554.

Find attached the paper.

Best regards,

Many Thanks   to everyone ...

In my opinion, each individual criterion is insufficient to judge about model, e.g. a time series model. I prefer combining several criteria, especially significance of the parameters (using say t-student) is important, as well as the statistics on the residuals behavior, e.g. being white and normality.

See: A Systematic Fuzzy Decision-Making Process to Choose the Best Model Among a

Set of Competing Models

by Hamed Shakouri G. and Mohammad B. Menhaj

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 38, NO. 5, SEPTEMBER 2008

Why not try understanding the autocorrelation structure first - often you do not need to include all of the autoregressive lags in a model, but only selected ones up to a maximum lag (or embedding dimension). Boix & Jenkins write a lot about how to analyse Autocrrelation and Partial Autocorrelation Functions (visually), in Engineering Spectral Analysis is used to understand the most important lags. Then you may derive a number of valid candidate models and can compare their adequacy using the criteria you mentioned above. Hope this helps, Sven

You can follow the David Hendry  General to Specific  (G2S) modelling technique. Selecting more general model and then applying restriction on lags to get parsimonious model

Fantastic contributions, you guys have really helped me.

If you have a large sample size, and a model with high autocorrelation and high kurtosis, you may use the Newey-West lag selection scheme (  see Newey and West, 1994).

I really appreciated this discussion. My preference in selecting lag structure goes also to David Hendry general to specific procedure complemented with conventional diagnostic tests. Otherwise the other combined tests may provide conflicting results.

Following...

Very fruitful discussion. So far I am using aic, sic, and sometime hendry general to specific, and my decision is depend on number of observation and number of variable that I employed.

A very helpful discussion. As for now in my case apart from other formal techniques in lag estimation identification, observing a time series plot can also give you an intuition of possible lag variables to include in the modelling process. I used a Weka forecasting package, the good thing is that it uses machine learning algorithms for time series forecasting. There is a custom lag variable which a user can specify that you think can improve model results. I run different experiments with different lag estimations and conclude depending on performance evaluation between training and testing. Example if i have a weekly time stamp data for 4 years, i can specify a lag variable of the previous year (1-4,52-56 i.e previous 4 weeks plus same weeks last year)and evaluate my results to see if previous year lag variable have improved model performance or not.

Although further improvements needs to be done as this approach can not guarantee efficient and effectiveness of the results. There is a need for automation process is lag selections(for Weka package).

Just one point. Information criteria say of course nothing about the statistical properties of residuals. I think the best is to combine information criteria and whiteness tests. First for a range of lags estimate models, and keep the ones having only sperical disturbances. Next, among these models use the AIC to chose. Also I don't believe such information criteria to be very reliable, AICc our AICu seems to perfom better in small samples. See also top-down or bottom-up methods

This is tough. I think the most important thing to do is think through your model: how long should it take for one variable to affect another? This is a theoretical, not statistical issue.

A quick and dirty method is to plot x(t) vs. x(t - tau). If your data are sufficiently oversampled, the points with tau = 1 should cluster around a 45-degree line. Increase tau until the plot begins to approach circular symmetry but no further. That value of tau is a good choice for most purposes. If the data are undersampled, use tau = 1 and hope for the best. If whatever you are trying to calculate depends strongly on tau, you have an ill-posed problem that finding the "best" value of tau cannot solve.

It depends on 2 things, (i) the frequency spectrum of your time series and (ii) the sampling rate used. There are several techniques, depending on what model you want to use. For autoregressive modelling start with Akaike's Information Criterion, AIC.

Thanks Fernando.

Most important is to think about question you are answering. What you need is simple to answer what time is needed for variable to evolve and to have impact on variable you are looking. After that experiment your thesis. Then try again, and again....

I gain a lot through this discussion, thank you all

You are welcome Abas.

Jamal

Visualise your data and ask yourself "how much do I need to look into the past to estimate what happens next"? Simple.

Very helpful discussion.

Thank you all

Generally, the lag selection criteria depend upon the researcher its self. The researcher needs to reveal the criteria in their research paper on the basis that the analysis has done.

it is quite common to have contradictory results coming from different criteria. For example SBC penalized model complexity more heavily than any other measure and might therefore give a different conclusion. However, a model that outperforms another in several of these criteria might generally be preferred.

See: Applied Econometrics, A Modern Approach by Dimitrios Asteriou and Stephen G Hall.

I fully agree with Shahnawaz Karim that is ..."information criteria are the initial measures that can be adopted when selecting the appropriate 'lag length' in a time series. However, we can get conflicting conclusions regarding the 'lag length' when these criteria are used. Let me clarify using the example of estimating a VAR model. Firstly, one should use a sufficiently large number of lags when estimating a VAR model, of course depending on the number of observations. Secondly, he should test if the same model can be estimated with fewer lags on the variables included. Thirdly, he can test the cross equation restriction using the 'Likelihood ratio' test. If the LR test decision goes in favor of a more restricted model, we should estimate the VAR model using fewer lags. Hence appropriate lag lengths can be chosen by paring down the 'lag length' using the 'likelihood ratio' test, especially when the sample size is not small..." . One crucial point from my point is the specification of the used VAR in order to find out the optimal lags. I think that the variable included in VAR should be estimated on levels, not in the first differences ...At the second step, if we finally conclude about the lags... then of course the VAR should be estimated based on stationary series ( eg in Dlogs)....in order to avoid spurious regression problem....

Lag determination always goes with data and an underlying model. At the end of the day the issue is that the data given follow the given model with order equal to the lag.

Lag determination always goes with data and an underlying model. At the end of the day the issue is that the data given follow the given model with order equal to the lag.

You could use the rule-of-thumb

One should apply various methods as discussed above, but the decision should be based on the principle of parsimony or minimum number of lags.

use all criteria cited above and after that take the smallest lag length from them.

The rule is to select the criterion with the lowest value which is the AIC at 26.90693 this is because the lower the value, the better the model. We can conclude that the optimal lag length for the model is 2 and the best criterion to adopt for the model is AIC.