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Re: q: Code for GARCH model in Mathematica

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  • Subject: [mg77019] Re: q: Code for GARCH model in Mathematica
  • From: Ian Gregory <newsgroups at>
  • Date: Thu, 31 May 2007 03:41:49 -0400 (EDT)

For univariate GARCH there the timeseries package in Mathematica uses a BHHH algorithm to find a solution.

However, the main function ConditionalMLE (which obtains 'optimum' coefficients) does not respect non-negative coefficients on the ARCH and GARCH terms as shown by Bollerslev (1986) since the routine can terminate normally with negative coefficients.
There is an example to place restrictions on parameters loglikelihood function and can be found in the timeseries documentation (2006 version) p.192.  But this does not directly tackle the problem.

A suggestion to avoid the negative coefficients is to use the format: (x,xstart,xmin,xmax) in the Findminimum documentation:

FindMinimum[-LogLikelihood[data, ARCHModel[{a0, a1}]], {a0, 0.5, 
      0.01, 5}, {a1, 0.5, 0, 5}]

Thank you,

Ian Gregory.

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