GARCH with variables

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nerijus
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GARCH with variables

Postby nerijus » Wed Dec 10, 2008 2:23 am

Hi guys, sorry for my english.

I'm complete beginner in time series. I'm trying to measure the impact of macro announcements on volatility. I have ~72000 observations (EUR/USD returns, 5 minute intervals) and ~1000 news, which are in 12 categories. I need to analyze the impact of these categories on return volatility. As far as I understand these categories can be represented as dummy variables. Where should I include dummy variables, in conditional mean or in variance? I've read a lot of studies (including Engle's and Bollerslev), but more i read, more i'm confused. I don't need any complex system, the simpliest would be the best, but the GARCH model is necessary.The biggest problem is that I have no time to learn software languages like eviews, R, MATLAB etc, and i need to test the impact of news as soon as possible. Maybe somebody has written such or similar program or can suggest the easy way to do that? Or maybe where is someone who can help me to do the calculations? I wouldn't remain in debt...

trubador
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Re: GARCH with variables

Postby trubador » Wed Dec 10, 2008 5:08 am

GARCH has two parts that you should estimate simultaneously. First part is called "the mean equation", which you can define your stationary time series as univariate and/or as a function of other independent variables. In this part, however, it is assumed that the squared disturbance/error term is not white noise and therefore should be modelled seperately. In the second part, which is called "the variance equation", you can specify the structure of your error term as a GARCH-X process. Since you are looking for the impact of "news" on the volatility, you should include your variables in the variance equation. Using EViews is really the easiest way of conducting an ARCH analysis:

1-Open your EViews program and create a workfile that contains all your variables.
2-Select "Quick/Estimate Equation" from the above menu.
3-Select ARCH in "Estimation Settings" below in the Equation Estimation dialog box you have opened.
4-Define your "mean equation" (e.g. AR(1)).
5-Select an appropriate method (e.g. GARCH(1,1)) and put your exogenous variables into "Variance regressors" edit box.
6-Estimate and make sure that there are no autocorrelations left in the residuals and the squared residuals.

If you decide to go a little bit deeper, I suggest you to build an EGARCH(1,1) model with asymmetric order of 1, since positive and negative news might have different effects on the volatility.
Last edited by trubador on Wed Dec 10, 2008 8:38 am, edited 1 time in total.

nerijus
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Re: GARCH with variables

Postby nerijus » Wed Dec 10, 2008 7:46 am

Thanks trubador very much. I think I'm on the right way. One more question about these exogenous variables. I didn't find clear explanation what they are. As I understand they can be like difference between forecasted and actual macroeconomic statement in my case, right? Can they be dummies (1;0)? If no, is there any possibility to work with dummies in GUI?

trubador
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Re: GARCH with variables

Postby trubador » Wed Dec 10, 2008 8:56 am

Any stationary variable would suffice, but in your case, it should be better to include them as dummy variables. Actually, you have 13 distinct categories of events including no news. In other words, your base for comparison is the no news situation. You can code each of your exogenous variable as a binary (e.g. 0-1) dummy variable, which correspond to variance regressors. Dealing with qualitative data is really a difficult task. For instance, it might be important to make a distinction between good and bad news. Moreover, expectations play a crucial role in such circumstances...

nerijus
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Re: GARCH with variables

Postby nerijus » Thu Dec 11, 2008 12:20 pm

I'm doing something wrong.
In excel i calculated reruns as R(t)=ln(P(t)/P(t-1)). Column "news": news = 1, no news = 0.
In eviews mean equation i write: R ar(1); news included in variance regressors. I get:

AR(1) -0.058436
Variance Equation
C 1.34E-08
RESID(-1)^2 0.103805
GARCH(-1) 0.792424
NEWS 3.76E-08

R-squared 0.001148
Adjusted R-squared 0.000984
S.E. of regression 0.000376
Sum squared resid 0.003450
Log likelihood 158655.3

1) How to interpret NEWS coef.?
2) When i look to actual, fitted, residual graph, I see that actual and residual graphs are almost identical. What am I doing wrong?

Gene
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Re: GARCH with variables

Postby Gene » Thu Dec 11, 2008 1:49 pm

nerijus wrote:I'm doing something wrong.
In excel i calculated reruns as R(t)=ln(P(t)/P(t-1)). Column "news": news = 1, no news = 0.
In eviews mean equation i write: R ar(1); news included in variance regressors. I get:

AR(1) -0.058436
Variance Equation
C 1.34E-08
RESID(-1)^2 0.103805
GARCH(-1) 0.792424
NEWS 3.76E-08



1) How to interpret NEWS coef.?

when there is news the conditional volatility is 3.76e-8 higher than when there isn't.

2) When i look to actual, fitted, residual graph, I see that actual and residual graphs are almost identical. What am I doing wrong?


You are not neccessarily doing anything wrong. why do you expect actual to change? Isn't it the original dependent variable? If the additional variable does not change the mean equation estimation much, adding the News variable to your volatility equation doesn't neccessarily have to change the residual,fitted data much. If you delete the News variable does your AR(1) coefficient change much? If not, then you shouldn't expect fitted residual graph to change.

nerijus
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Re: GARCH with variables

Postby nerijus » Thu Dec 11, 2008 2:19 pm

I don't expect actual to change. Now residuals = actual. How can it be so? It does not matter if I include news in variance or not, also it does not matter what lags of ar process i use, every time residuals are the same as actual (sometime the is difference about 0,000000001). Aren't residuals what's left after fitting the model to data?

EViews Gareth
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Re: GARCH with variables

Postby EViews Gareth » Thu Dec 11, 2008 2:44 pm

If your model is a terrible model, then the residuals will be close to the actuals. Your R^2 doesn't exactly instill a lot of confidence in the model...
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startz
Non-normality and collinearity are NOT problems!
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Re: GARCH with variables

Postby startz » Thu Dec 11, 2008 2:52 pm

QMS Gareth wrote:If your model is a terrible model, then the residuals will be close to the actuals. Your R^2 doesn't exactly instill a lot of confidence in the model...


No no no. The R^2 close to zero inspires a lot of confidence in the model. Returns are close to unpredictable, therefore the R^2 should be nearly zero.
Of course, this means that you should be happy that the actuals and the residuals are about the same. (Note you might have something to say about volatility nonetheless.)

EViews Gareth
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Re: GARCH with variables

Postby EViews Gareth » Thu Dec 11, 2008 2:59 pm

Hmmm, you're on a slippery slope there, if you're going to start bringing in real world interpretation into econometrics, who knows where we might end up.
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nerijus
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Re: GARCH with variables

Postby nerijus » Thu Dec 11, 2008 3:18 pm

It's simple AR(1)-GARCH(1,1) model. I didn't imagine and still don't that it could be so terrible. arma (p,q) with garch(1,1) variance gives the same results - actual=residual. Can both models be so terrible? Is everything ok with spec. in means:
R ar(1)
R ar(1) ma(1)
Maybe I miss something in the mean equation?

I don't know why I should be happy, contrary, I'm VERY SAD. How can then I explain news impact on volatility? And news coef. is so small, actual too small to be true. I still think i miss something.

startz
Non-normality and collinearity are NOT problems!
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Re: GARCH with variables

Postby startz » Thu Dec 11, 2008 3:23 pm

nerijus wrote:It's simple AR(1)-GARCH(1,1) model. I didn't imagine and still don't that it could be so terrible. arma (p,q) with garch(1,1) variance gives the same results - actual=residual. Can both models be so terrible? Is everything ok with spec. in means:
R ar(1)
R ar(1) ma(1)
Maybe I miss something in the mean equation?

I don't know why I should be happy, contrary, I'm VERY SAD. How can then I explain news impact on volatility? And news coef. is so small, actual too small to be true. I still think i miss something.


If you don't mind making your data public, you might post your workfile as an attachment for others to look at and make suggestions.

trubador
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Re: GARCH with variables

Postby trubador » Thu Dec 11, 2008 3:28 pm

1-You should examine probabilities for significance instead of levels of coefficient estimates. Statistical significance is more important than magnitudes. You are using logarithmic difference of series in the mean equation, and square of the residuals in the variance equation. So you should expect small figures.

2-If the coefficients of ARMA(p,q) process are not significant, then residuals and actual series can be more or less equal. This is usually the case in high frequency financial data, especially when you are using log-return of series. As a final remark, it is generally suggested to include a constant term in your mean equation in order not to force the model towards the origin...

nerijus
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Joined: Wed Dec 10, 2008 1:59 am

Re: GARCH with variables

Postby nerijus » Thu Dec 11, 2008 3:40 pm

Here is simplified example. Still i need to make few corrections in data, but it does not change the point.
Attachments
sample.xls
(500 KiB) Downloaded 784 times

startz
Non-normality and collinearity are NOT problems!
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Re: GARCH with variables

Postby startz » Thu Dec 11, 2008 7:18 pm

trubador wrote:1-You should examine probabilities for significance instead of levels of coefficient estimates. Statistical significance is more important than magnitudes. You are using logarithmic difference of series in the mean equation, and square of the residuals in the variance equation. So you should expect small figures.

2-If the coefficients of ARMA(p,q) process are not significant, then residuals and actual series can be more or less equal. This is usually the case in high frequency financial data, especially when you are using log-return of series. As a final remark, it is generally suggested to include a constant term in your mean equation in order not to force the model towards the origin...


Let me disagree on one piece. The difference between the actual variables and the residuals generally depends on the magnitude of the coefficients, not their statistical significance.


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