Garch with dummy in mean equation

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

[Walter Roberson]

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]

I deleted my previous erroneous comment.

Answer 1

[the cyclist]

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.

Answer 2

[Oleg Komarov]

% 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]);

Answer 3

[gaia buratti]

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

[Oleg Komarov]

Are you doing garch at all?

Anyways, as you say you don't have to do MA, just change specification.

[gaia buratti]

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]

* 4 dummies for the quarters? Which book are you using?

[gaia buratti]

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]

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]

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]

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]

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