[R-SIG-Finance] Update of rugarch package yields different results / questions on stationarity conditions

[alexios ghalalanos]

Unless you tell us what the previous version you had installed was, I
really can't say for sure.

1. Is for the stationarity of the eGARCH model.
2. Are the parameter bounds.

You are free to change both:
1. can be switched off by setting fit.control$stationarity=0
2. can be changes to whatever you want by using the setbounds<- method
on the specification.

As far as I know, you can take the ARMA and GARCH stationarity
conditions separately, as you can also estimate them in 2 steps
without too much loss in efficiency. If you want to see the degree of
interaction between the 2, then use the ugarchdistribution method which
includes a number of interesting parameter interaction plots (and you
can also investigate others by working with the returned parameter
distribution data).

If you feel there is some bug somewhere in the code or you have some
suggestion how to make the estimation of a certain model 'better', then
by all means feel free to contribute a detailed patch.

-Alexios


On 24/09/2014 20:01, Stefan.Jaeschke at rwe.com wrote:
> Hi there,
> 
>  
> 
> 1)     I have recently updated the rugarch package to version 1.3-3 (I
> do not remember the previous number) and I am surprised to see different
> results when fitting a dataset, the loglikelihood is lower than before
> and the beta parameters have changed significantly. Below I put the code
> from the fit
> 
>  
> 
> Data <- read.csv("WTI_logreturnsUS.csv", header = TRUE, sep = ";", dec=".")
> 
> renditen <- Data$LogReturnsWTI
> 
> Data_WTI <- renditen
> 
> nrenditen = renditen - mean(renditen)
> 
> external <- Data$LogReturnsStocks
> 
> dim(external) <- c(length(external),1)
> 
> mean_WTI <- mean(renditen)
> 
>  
> 
> spec = ugarchspec(variance.model = list(model = "eGARCH", garchOrder =
> c(2,3), submodel = NULL, external.regressors = NULL, variance.targeting
> = FALSE), mean.model =list(armaOrder = c(0, 0), include.mean = FALSE,
> external.regressors = external), distribution.model = "sged")
> 
> fit <- ugarchfit(spec,nrenditen)
> 
>  
> 
>  
> 
> likelihood         2326.425          2319.141
> 
>                        
> 
> mxreg1             -0.3644             -0.3124
> 
> omega              -0.3081                -0.0474
> 
> alpha1              -0.1288                -0.1090
> 
> alpha2              -0.1308                0.0644
> 
> gamma1           0.2575                  0.2189
> 
> gamma2           0.2340                  -0.1441
> 
> beta1                -0.6917             0.9999
> 
> beta2                0.9764              0.4135
> 
> beta3                0.6738              -0.4199
> 
> skew                0.9659             0.9708
> 
> shape               1.9107              1.9373
> 
>  
> 
> Why do I see these differences?
> 
>  
> 
> 2)     Why do we need the following two conditions for strict
> stationarity of an EGARCH(q,p) model? I do refer to the ARMA
> representation in Nelson (1991), Equation (2.3)
> 
>  
> 
> a)     min(Mod(polyroot(c(1, -betas)))) > 1
> 
>  
> 
> b)    |beta_i| < 1, i = 1,…,p
> 
>  
> 
> Whereas condition a) is clear to me (stationarity of AR processes), I
> don’t see we should restrict the parameter |beta_i| < 1. Could somewhen
> help on that? Why are the parameters regarding q not involved in the
> conditions at all?
> 
>  
> 
> 3)     In general, I am aware of conditions for stationarity for
> conditional mean processes (e.g. ARMA-models) or conditional variance
> processes (e.g. GARCH-models). I am struggling a bit to find sufficient
> conditions for (strikt) stationarity in case of combinations. For
> instance, an ARMA(1,0)-GARCH(1,1) or ARMA(0,1)-EGARCH(2,3) model. Can I
> take the conditions for mean/variance separately and join them in the
> end? They should interact somehow, shouldn’t they? If anybody could help
> me on that, I would be very pleased.
> 
>  
> 
> Many thanks in advance!
> 
>  
> 
> Mit freundlichen Grüßen / Kind regards
> 
>  
> 
> *Stefan Jäschke*
> 
> RWE Supply & Trading GmbH
> 
> Performance Controlling CAO Gas & VAC (MFC-GV)
> 
> Altenessener Str. 27
> 
> 45141 Essen
> 
> Germany
> 
> Phone                      +49 201 5179-1674
> 
> Email                      stefan.jaeschke at rwe.com
> <mailto:stefan.jaeschke at rwe.com>
> 
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