I need to compare two garch models, I try to do that by Value at Risk. In general, if I have an initial conditional variance, for example, h1, then I can predict the next N days conditional variance by a known garch model, whereafter, I calculate the VaR based on these conditional variance and make the comparison between two garch models, simply saying, to see how many times the daily return exceeds the VaR. My question is that: do I need to make a one day ahead predict based on the standard deviation from real data (get it by high frequency method) each time? or just make N days prediction based on the initial h1. Thanks.

  • $\begingroup$ Depends on what criterion you want to compare the models: on their one-step ahead prediction error with expanding window (updating the model on each step) or with an in-sample (estimation) period and out-of-sample (validation) period. It's a design decision. $\endgroup$ – Jean-Paul Apr 15 '15 at 19:19
  • $\begingroup$ Thanks @Jean-Paul. I am do the test in-sample but not make the decision for future, then in your words, it is unnecessary to update each step? $\endgroup$ – Fly_back Apr 15 '15 at 19:40
  • $\begingroup$ If I understand correctly you only want to compare both GARCH models in-sample? In that case, it would make sense to simply calculate variance for the VaR estimate of the full in-sample period as well. For out-of-sample, it would make more sense to iteratively update your VaR distribution with an expanding window. $\endgroup$ – Jean-Paul Apr 15 '15 at 19:45
  • $\begingroup$ Yes, I just need to make a comparison. One more thing, if it is OK for you, @Jean-Paul. I have BIC for model A and model B and it shows A is better fit. But in the VaR test, the case is converse, is that reasonable? $\endgroup$ – Fly_back Apr 15 '15 at 19:47
  • $\begingroup$ Can you explain more precisely how exactly you are performing this VaR test? Because VaR will simply give you a certain threshold for each moment in time. If one model crosses this threshold more often than another model, we can not infer from this that one model is worse than the other model. After all, you are trying to estimate volatility. Because volatility is unobserved, comparing it to crossing the VaR threshold is not very informative. Instead, VaR is meant to estimate a risk factor based on historically realised returns, not volatility. $\endgroup$ – Jean-Paul Apr 15 '15 at 19:58

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