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I'm an italian student using rmgarch package for forecasting covariance matrix. While using ugarchspec function for defining input parameters of univariate GARCH model using a t-Student distribution, I have noticed that there is a parameter called fixed.pars. Following the example given in GitHub this parameter is set as following:

fixed.pars = list(shape = 5)

in case of a t-Student distribution. If i change this setting from 5 to 3 (for example) results are very different: can someone tell me the importance and the usage of this parameter?

Thanks to all

Tommaso Ferrari
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1 Answers1

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So I think you're using parameter two different ways here. fixed.pars is an argument that allows you to fix one or more parameters from the distribution. fixed.pars allows you to conduct statistical tests on the parameters (see https://stats.stackexchange.com/questions/234738/dcc-garch-how-to-test-restricted-vs-unrestricted-model-with-lr-test) and is required to run some DCC functions (see https://cran.r-project.org/web/packages/rmgarch/rmgarch.pdf).

For the shape parameter (https://en.wikipedia.org/wiki/Shape_parameter), uGARCHmultispec finds a common shape parameter based on your input list of univariate GARCH specifications. Using fixed.pars largely overrides that process and restricts the shape to whatever you specify it to be. You can see the effect of changing shape parameters on different distributions at http://www.randomservices.org/random/apps/SpecialCalculator.html.

cgrafe
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  • Dear @cgrafe, thanks for your answer! According to your link, I can suppose that the shape parameter is linked to degrees of freedom of the t-Student distribution. I have never heard of "shape", but I have always referred to t-Student using its degrees of freedom. In other words, can I assume that the parameter "shape" I'm passing to the function represents the number of degrees of freedom of the distribution? – Tommaso Ferrari Aug 09 '19 at 06:46
  • Not exactly, as I understand it. The shape is determined by the degrees of freedom, but the shape parameter (in the multivariate t distribution) is derived from your univariate inputs. You can see the shape matrix and relationship to df in the upper right at https://en.wikipedia.org/wiki/Multivariate_t-distribution. – cgrafe Aug 10 '19 at 03:38