Garch with dummy in mean equation

2011 8 11
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Hi, I would like to estimate this regression y=aD1 +aD2 + BD1Ret + BD2Ret +e. D1 is a dummy that is 1 whrn the return is positive, whereas D2 is 1 when it is negative and zero when is positive. I want to use a garch model. Is it correct to put in the garch specification 'C' NaN and to put in the matrix with the dependent variable D1 and D2, i this way it should ignore C and the intercept would become the coefficients of D1 and D2.
I know that i could set the equation as y=a +aD2 + BRet + BD2Ret +e. but I prefer have the two different coefficient and tyhen compute the difference. Thanks in advance Gaia

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Walter Roberson
Walter Roberson 2011-8-11
Is that the U-shaped piece of logic that you have to get the plumber to come over and clear out if you don't run the garbage collector often enough?
Oleg Komarov
Oleg Komarov 2011-8-11
I deleted my previous erroneous comment.

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the cyclist
the cyclist 2011-8-11

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I don't know the specific answer to your question, but I use a general approach that might be useful to you: Generate data that you know should be perfectly fitted by the model you propose, then see if the technique you want to use gives the correct result.

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Oleg Komarov
Oleg Komarov 2011-8-11

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% Fake returns
R = randn(1000,1);
% Intercept dummy
D1 = R > 0;
% Coefficient dummy
D2 = zeros(size(R));
D2(D1) = R(D1);
% GARCH(1,1) with MA(1) for mean + dummies
Spec = garchset('M',1,'P',1,'Q',1,'Display','off');
garchfit(Spec,R,[D1 D2]);
gaia buratti
gaia buratti 2011-8-11

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Thanks to both. Oleg, I think that your model is good for the moving average, but I don't have to do a MA, I have to regress against other variables, like y=a+Bx+e but with dummies. By the way I empirically tried as the cyclist suggested and it seems working. It is a good method, I didn't think about it, I'm sorry but it is my first "empirical work ".
Gaia

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Oleg Komarov
Oleg Komarov 2011-8-11
Are you doing garch at all?
Anyways, as you say you don't have to do MA, just change specification.
gaia buratti
gaia buratti 2011-8-11
ok, I've jusr seen now your firsst comment about the dummy trap, you mean when you put both the dummies and the whole period? i use the example of the book, when you want to test seasonality and you use the 4 dummies for the quarters plus the constant?
If it is, I checked it is not my case, iI could use the whole period plus the dummy for the negative returns or 1 for the negative and 1 for the positive, just change the interpretation.
Btw I use the Garch specification for the regression because the residuals follow an arch model.
Oleg Komarov
Oleg Komarov 2011-8-11
* 4 dummies for the quarters? Which book are you using?
gaia buratti
gaia buratti 2011-8-11
I' m sorry I didn't explain very well , what do you mean with "dummy trap" because before setting that model I reviewd everything about dummies to be sure to avoid mistakes.
Oleg Komarov
Oleg Komarov 2011-8-11
Ok,sorry gaia, I take back the dummy variable trap thing. I misread your first equation.
Yes, about the 4 dummies + constant = trap.
gaia buratti
gaia buratti 2011-8-11
Ok, perfect, btw, since I see you know preatty well the subject, do you think that using the dummies in the mean regression and use the garch model to correct for heteroskedasticity can be a problem? In other words, the GARCH works well even if there are dummies?
Briefly, my dependent variable is the cross-sectional absolute deviation(CSAD) that I am regressing on the abs returns and also on the squared ones. To dettect any asymmetry between up/down mkt i used the dummies, in the previous equation I forgot the one for the intercept. and my equation results
CSAD=aDu+aDd+B|R|Du+B|R|Dd
Du= 1 when ret >0.
Thank you
Oleg Komarov
Oleg Komarov 2011-8-11
Shouldn't give you problems but don't take my words for granted. I am no expert in ARCH modelling, just know how to implement it with MATLAB.
gaia buratti
gaia buratti 2011-8-12
Thanks, it was jusr a confirmation, I spent a day looking for an answer but I didn't find anything... I reasoned about that and i don't think it creates...I hope

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