I'm studying the monetary transmission mechanism, using 4 variables(inflation, interest rate, exchange rate and gnp), through impulse response functions
When using Akaike, Hannah-Quinn and Schwarz information criteria, they suggest the use of 3,3 and 1 lag(s). But these models(and the model with 4 lags, a competitive one according to the IC) all did not pass on autocorrelation, heterokedasticity and normality tests(even though the last one is widely reported as 'commom' in this context).
When using larger lag lenghts(9 through 12), the autocorrelation problem disappears, even though non-normality and heterokedasticity remains.
Should I use the information criteria suggestion and work through the model with 3 lags, for example, correcting him, or should I use the model with more variables with 1 less problem? I have a large sample(277 with 12 regressors), so size should not be a problem.
Your results are kind of common in this branch of the literature, but this is not fully addressed in the published papers. First, I would like to have all the disturbance's maintained properties somehow favored by the data. Second, once data is rejecting maintained properties, you can either see estimate (i) an heterokedastic VAR model (see the 'recent' NBER paper from Hamilton about conditionally heterokedastic VAR models), (ii) a Non-normal VAR by maximum likelihood, and/or (iii) estimate a non-normal heteroskedastic VAR model. This way is nice because then the maintained properties are not so important. A key issue, though, is the one related to parsimony, but there is a recent literature on parsimonious VAR models that uses penalized maximum likelihood estimation. There are many options here, so I would ask for recommedations from any researcher who has explored these options. Finally, it is possible that some of the conditions behind AIC or any other IC cririteria do not hold for the specific task of selecting the optimal VAR system's lag.
Assuming that you don't have a very long series, I would choose the shorter lag, i.e. I mostly trust the BIC which leads to a parsimonous model.
However, if you get more appealing results for longer lags (i.e. consistent with your economic interpretation) - feel free to choose it in a different way.
Paweł Baranowski my series has 240 observations, not super large but I think enough to use 12 lags, if necessary. I'm inclined to use 12 lags, as of now.
Carlos R. Barrera-Chaupis just read the Hamilton article, very interesting. Was going to trust White's standard errors, but now will take a closer look.
Thank you both for your responses.
Brenno Machado
The purpose of choosing optimal lag is to reduce residual correlation. Literature provises various choices such as Akaike, Hannah-Quinn and Schwarz information criteria and Sim's Likelihood test. There is no best one. At lags 9 through 12, you have no residual correlation so you should start with 12 and use AIC or SIC to select your model. The key point is not to loose site of your goal and that is reduction of serial correkation.
After that, you now have a selected model and at this stage you can take care of normality problems using various dummies based on what has happened in the economy. I start with standardized residul which will identify the outliers and then I must include AFC and GFC (key crsis)
Using VAR, the optimal lag is that which has the minimum value as reported by each of the criterion. That is AIC, SIC, HQ or FPE. If the criteria are showing different lags, you're at liberty to use either of them.
I don't work with VARs anymore but to just use 12 regressors all at once doesn't seem reasonable to me . I don't think it's possible to infer what's really causal or atleast significant because of all the dependence and lack of residual normality
that will most likely show up. So, my one suggestion is to start out with a small number of regressors and work your way up. Even 4 to me sounds high to start out with. If a simple VAR model ( say 2 or 3 variables ) doesn't look reasonable in some sense, then adding onto that model by using ONE MORE variable, may not help much either. But atleast that way is biased towards parsimony.
Henry and Leed has made valid points. However, Leed's argument is fundamental. Using 12 regressors may bias your VAR result. Also, adopting Leed's suggestion of working up from smaller number of regressors may also change the idea of your study and limit its methodology (you're the conceptualist and should always bear in mind your objective).
I suggest you consider structural VAR (SVAR). Structural equation modeling (and its modifications, such as SVAR, S-GARCH) is unique for its ability to utilize large samples and variables without biasing the result (once you confirm model fit).
Therefore, using structural VAR, you're able to continue with 12 regressors and over 250 observations, while adopting James Tumba Henry's recommendation for choosing optimal lag length.
Valentine. That's good to know but I''m not familar with Structural VARS. I do have the Lutkepohl and Kilian book but noi time to read it right now. I would like to get a clue about them so do you know of a smaller intro document that explains what they are just to get the basics. Thanks.
Basically, optimal lag selection is to make VAR models parsimonious. What is your data frequency? if its monthly, check maximum lag length of 24 and trim it down.. similarly you can do for quarterly also . I think you data would be monthly and you are giving less than the required optimal lag length for checking even!!
Mark, you can check Ahelegbey, Billio and Casarin (2015) for Bayesian graphical SVAR and Okolo and Udabah (2019) for applied graphical S-GARCH
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