Implementing component GARCH process

[RichardMM]

This implements the Engle & Lee 1999 Components GARCH model which decomposes volatility into long term and short term components.

A lot of change has been in the volatility.py and recursion.py files but parts of base.py and mean.py have been modified but only slightly to handle a volatility process that generates two volatility series.

Tests have been added to test forecasting, representation, recursion, and estimation of CGARCH.

Forecasting is enabled for CGARCHbut only analytical method. Other methods will be included later.

One example has been put in the Examples folder and the docs have been changed where needed to show the new functionality.

[coveralls]

Coverage decreased (-0.5%) to 98.238% when pulling 580ae56 on RichardMM:master into ef52881 on bashtage:master.

[coveralls]

Coverage decreased (-0.5%) to 98.238% when pulling 580ae56 on RichardMM:master into ef52881 on bashtage:master.

[codecov]

Codecov Report

Merging #188 into master will decrease coverage by 2.27%.
The diff coverage is 77.77%.

@@            Coverage Diff             @@
##           master     #188      +/-   ##
==========================================
- Coverage   99.36%   97.08%   -2.28%     
==========================================
  Files          72       35      -37     
  Lines       13285     8728    -4557     
  Branches     1131      780     -351     
==========================================
- Hits        13201     8474    -4727     
- Misses         28      159     +131     
- Partials       56       95      +39     

Impacted Files	Coverage Δ
arch/univariate/base.py	93.13% <47.22%> (-4.50%)	⬇️
arch/univariate/recursions_python.py	84.87% <72.72%> (-13.73%)	⬇️
arch/univariate/volatility.py	95.77% <75.92%> (-3.39%)	⬇️
arch/univariate/mean.py	92.97% <80.00%> (-5.34%)	⬇️
arch/univariate/recursions.pyx	94.64% <85.71%> (-5.36%)	⬇️
arch/tests/univariate/test_volatility.py	99.76% <96.87%> (-0.24%)	⬇️
arch/utility/array.py	81.81% <0.00%> (-13.81%)	⬇️
arch/unitroot/unitroot.py	93.39% <0.00%> (-5.51%)	⬇️
... and 71 more

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[bashtage]

Thanks for making these changes. I'm not sure this is the simplest method to implement Component GARCH since the standard Component GARCH is just a restricted GARCH(2,2). This said, I hanve't carefully reviewed these changes and so these might be more general.

[RichardMM]

I didn't want to modify the GARCH class to allow for a restricted GARCH(2,2) because it's a really loaded class, adding it there would make it even more complicated, so I opted for a separate class altogether.
Thanks for the response

[bashtage]

I think it should be possible to subclass GARCH setting p=q=2, and then overwriding some of the methods to specialize for the different parameter interpretations (e.g. that starting values, likelihood, etc). I think many of the methods, aside from handelign the mapping between CGARCH parameters and GARCH(2,2) parameters, will be unchanged. These could be written in a manner like

def some_func(self, params):
    tparams = self._transform_params(params)
    return super(CGARCH,self).some_func(tparams)

[RichardMM]

With subclassing , I think it would get problematic with methods that deal with the long term component e.g compute_variance and _analytic_forecast because how would one change the super(CGARCH,self).some_func(tparams) to return the long term component even if we transform parameters.

[coveralls]

Coverage decreased (-0.5%) to 98.196% when pulling 1d2d55a on RichardMM:master into 3d3b390 on bashtage:master.

[RichardMM]

Hello, are you still considering this pull request?

[coveralls]

Coverage decreased (-0.5%) to 98.179% when pulling f0f65c5 on RichardMM:master into 2db76fa on bashtage:master.

[coveralls]

Coverage decreased (-0.5%) to 98.179% when pulling f0f65c5 on RichardMM:master into 2db76fa on bashtage:master.

[bashtage]

I haven't forgotten about this -- just been quite busy.

[RichardMM]

Hello;
Is there anymore needed from my end

[SvenEck]

Hi guys,

Is this topic still being pursued?