Update of rugarch package yields different results / questions on stationarity conditions

On 24 Sep 2014, at 22:02, <Stefan.Jaeschke at rwe.com> wrote:

Alexios, you provided me with this estimates back in a mail on Tues. 29.10.2013 13:46. And I could reproduce those values, now I am a bit irritated. Unfortunately, I am not able to rebuilt the "old" rugarch version.

-----Urspr?ngliche Nachricht-----
Von: alexios ghalalanos [mailto:alexios at 4dscape.com]
Gesendet: Mittwoch, 24. September 2014 19:47
An: J?schke, 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

If I were to actually use your previous estimates and filter the data you provided:

cf=list(mxreg1=-0.3644,

omega=-0.3081,
alpha1=-0.1288,
alpha2=-0.1308,
gamma1=0.2575,
gamma2=0.2340,
beta1=-0.6917,
beta2=0.9764,
beta3=0.6738,
skew=0.9659,
shape=1.9107)

setfixed(spec)<-cf
likelihood(ugarchfilter(spec, nrenditen))

[1] 1051.357

This seems much lower and considerably far from what the estimated model gives. Are you sure you provided us with the correct parameter values and the same dataset you used before?

-Alexios

On 24/09/2014 20:29, alexios ghalalanos wrote:
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 Gr??en / Kind regards



*Stefan J?schke*

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>