[R-SIG-Finance] Update of rugarch package yields different results / questions on stationarity conditions
Alexios Ghalanos
alexios at 4dscape.com
Wed Sep 24 21:06:04 CEST 2014
These are default bounds, and sufficient for the (q,1) eGARCH model to be stationary.
Generally, all parameters are given bounds since the optimization is constrained and the solvers used require parameter bounds (where defaults were chosen were possible to speed/ease estimation).
Alexios
> On 24 Sep 2014, at 21:58, <Stefan.Jaeschke at rwe.com> wrote:
>
> The version was the most updated one during end of October, 2013.
>
> Why are these bounds for beta set to (-1,1)? This has nothing with a stationary constraint, does it? Or would this somehow explode the model?
>
> -----Ursprüngliche Nachricht-----
> Von: alexios ghalalanos [mailto:alexios at 4dscape.com]
> Gesendet: Mittwoch, 24. September 2014 19:30
> An: Jäschke, Stefan; r-sig-finance at r-project.org
> Cc: alexios at 4dscape.com
> Betreff: Re: [R-SIG-Finance] Update of rugarch package yields different results / questions on stationarity conditions
>
> 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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