lag length selection criteria in determining the autoregressive lag length. The finding of this lag selection is that Akaike's information criterion (AIC) and final prediction error (FPE) are superior than the other criteria.used lag length is that which is most selected by the criterion named after the econometricians who developed them, like HQ, SIC, AIC and LR, etc. Some researchers prefer Schwartz criterion when the variables are more than 4 and use the AIC when the variables are less than 4. Generally, we choose the lag length for which the values of most of these lag length criteria are minimised, indicated

P. Sameerabanu, Thank you!

But how to know which number to add at the beginning? I have 29 years of data. Should I start from two and look? Even when I choose 9, I still have new criteria!

The asterisks below indicate the best (that is, minimized) values of the

respective information criteria, AIC = Akaike criterion, BIC = Schwarz

Bayesian criterion and HQC = Hannan-Quinn criterion.

Lags

log Loglik AIC BIC HQC

1 -437.67561 18.109209* 18.340860* 18.197097*

.........................

..............

AIC, BIC and HQC are significant at lag 1. that is simple view

Hi, Mohammed

Conventionally, in accordance with the information criteria (AIC, BIC....)

in your case of time series data, for the monthly data AIC works better, for quaterly and annual data BIC is more preferable....

Generally speaking, there may be a priori criteria which would lead you to a preferred answer (e.g., using quarterly data, you might choose 4 lags to pick up seasonality). Empirically speaking, I would start with the highest number of lags that (a) makes economic sense and (b) the data allows (e.g., from your description I would say 4 lags is sufficient). As you incrementally reduce the number of lags, if the AIC (or alternative) criterium reduces, this indicates a superior form of the model. Stop when the criterium does not improve.

Richard Hickling That's what I wasn't sure about. I started with 9 lags; four criteria noted that 8 was the right lag number. But then, I decided to lower the number and every time the optimal number of lags changed! I tried to read about which lag number is the right one but couldn't find a good reference.

Information criteria are often used as a relatively quick way of identifying the optimal VAR lag length and the contributions above provide guidance on these. If there is uncertainty (ambiguity) over which lag length to choose you may wish to apply misspecification tests to determine whether any identified lag length is consistent with a model that satisfies underlying assumptions of a well specified model (no autocorrelation, no heteroscedasticity etc). Software packages often have system (and equation) tests that can be applied. I would suggest you consider applying a system test for (at least) autocorrelation to ensure any chosen model is not evidently misspecified. You may wish to consider some of the other available misspecification tests too.

Dear Mohammad Jaber. You should mention the frequency of your data and how you proceed. Don't forget that, since you have 2 variables, you loose 4 degrees of freedom for each lag. I am therefore sure you have at least quarterly data because otherwise with 29 observations you should not afford more than 7 lags (29 - 7x4 > 0). When you run a selection, I suppose you set the maximum lag, say L, and then fit with L, L - 1, ... lags. Of course, the L first observations are lost in the procedure and this explains why you have distinct results when taking another value for L, that will loose a different number of observations. I hope this will solve your problem. Don't forget to look at residual autocorrelation also.

Guy Mélard Thank you for your answer, I have 29 years of annual data on energy consumption and GDP. I am trying to apply the Toda-Yamamoto non-Granger causality test to find the causal relationship between them.

What should I look for in the residual autocorrelation?

With annual data and so few observations, whatever your objective, I don't understand how you can consider a lag of 9. You will get a negative number of degrees of freedom! The absence of residual autocorrelation shows how well your model fits the data. For instance, if you had quarterly data and a lag smaller that 4, you could have autocorrelation at lag 4 because the model does not take seasonality into account. See Richard Hickling's answer.

Fit econometric models provide information as a first step. Based on economic theory, I would first establish the hypotheses of the relationship between the independent variables and the dependent one that I want to analyze in order to have the basis for analyzing the results.

I presume that you have real GDP and your energy consumption is in volume terms and that you are working with the log of both variables.

I would suggest that you go to your textbook and see if you can replicate the results of a lag selection example in the test book. It is difficult to give you a diagnosis without your data and your program. Otherwise, try a different econometric package (e.g. https://gretl.sourceforge.net/ which is free and user-friendly).

Treating 4 as maximum lags your criteria must be estimated using observations 5 to 29 as independent and 1 to 4 as lagged variables only, Treating 8 as maximum lags your criteria must be estimated using observations 9 to 29 as independent and 1 to 8 as lagged variables only, etc.

In ADF tests the maximum lag is often taken as

[the integer part of 12*(T/100)^0.25] which is 8 for 29 observations. See Hayashi, Econometrics page 592 and references therein. Many econometric packages used to use this as a maximum lag for determining lag length in this and other occasions. I would hope that with 29 observations it would specify a smaller number of lags as appropriate.

How can you justify economically that eight lags could possibly be valid? to add an extra lag to carry out this test. If you do not have cointegration then you use standard Granger tests and VAR in first differences. You will need strong economic arguments to justify the assumption that there are no other variables that are impacting both GDP and energy consumption. If there are such variables your test will not be valid.

How can you justify economically that eight lags could possibly be valid? There is something wrong with your model. The eight lags may be adjusting for autocorrelation caused by misspecification or an omitted variable. Unless there is something wrong with your calculations you need to rethink your model.