Avoid unnecessary complexity
1. Avoid unnecessary complexity
It is tempting to use the most complex GARCH model, such as the GARCH model with ARMA mean dynamics, a leverage effect in the conditional variance and a skewed student t-distribution. This complexity comes at the price of having to estimate a large number of parameters. The take-home message of this video is to use your intuition when specifying the model. If you know that the model is simple, then use a simple model.2. Avoid unneeded complexity
In particular, if you know that the mean dynamics are negligible, that the variance has no leverage effect, and that the distribution is symmetric with fat tails, then a standard GARCH model with constant mean and student t distribution is appropriate.3. Restrict the parameter estimates
You may also have a strong intuition about the parameter values. If you know that the parameters are equal to a certain value or, are inside an interval, then you should impose this in the specification using the methods setfixed and setbounds.4. Application to exchange rates
As an example, we take here the daily EUR/USD returns and estimate the constant mean standard GARCH model with student t distribution. There are five parameters for which you can see the estimates. Note that the estimated alpha is around 0-point-03 and that the estimated shape parameter is 8-point-8.5. Example of setfixed()
Suppose however that you know that the true value of alpha is 0.05 and that the distribution has 6 degrees of freedom. Then the alpha and shape parameters should not be estimated anymore. You can fix those values by applying the setfixed method on the ugarchspec object. The fixed values should be provided as a list. In the example, it’s a list of two elements with the alpha parameter equal to 0.05 and the shape parameter set to 6. You then see in the output that the fixed parameters are indeed at their fixed value, while the others have been estimated.6. Bounds on parameters
It also occurs often that you know that the parameter value is in some interval. The interval can be wide, such as the interval of all positive real numbers, as is the case for the omega, alpha and beta parameters such that the GARCH variance is a positive number. Sometimes the interval of plausible values is smaller. As an example, it can be that the only plausible values of alpha are between 0-point-05 and 0-point-2. Or that beta should be between 0-point-7 and 0-point-95. The 0-point-7 is then a lower bound, while 0-point-95 is the upper bound. Those bound constraints can be imposed using the setbounds() method.7. Example of setbounds()
The setbounds method requires to define a list. Each element in the list corresponds to the parameter that is restricted by the bounds. A vector of two elements is used to set the lower and upper bound.8. Use your intuition to avoid unneeded complexity.
To summarize, you need to use your intuition to avoid unneeded complexity when estimating GARCH models. Use your information to build simple models, to fix parameters or set bounds, and to impose that the GARCH dynamics are as you expect them to be. A special feature that you can impose is that the GARCH volatility fluctuates around the sample standard deviation. For the daily EUR/USD return this is 0-point-6%.9. Volatility clusters and mean reversion of volatility
Graphically, this means that the conditional volatility should be on average equal to the horizontal red line.10. Variance targeting
Mathematically, this means that the unconditional variance implied by the GARCH model equals the sample variance. To impose this in the estimation you need to set the argument variance.targeting to TRUE when specifying the variance model in ugarch spec. You can then see that indeed the unconditional variance implied by the model and the sample variance are nearly the same.11. Let's impose restrictions on the GARCH model
Since complexity has a price, let's find out how restrictions can help in GARCH modeling.Create Your Free Account
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