Estimation of VAR(1)-GARCH(1,1) model

[irfanawan]

Hello everyone,
I have data with outliers and without outliers of same financial series. Suppose I estimate the AR(1)-GARCH(1,1) separately on both series and come with different values of Log Likelihood values of both models. I want to apply Likelihood ratio test to compare the models and select the best one. I am confused with the degree of freedom of the test. Is the degree of freedom is 1 or 4 in this case?

Thanks,
Irfan Awan

[TomDoan]

Sorry. What are you trying to test? Series A estimates with series B estimates?

[irfanawan]

Dear Tom,
My question is, let suppose I have a data set of returns of any security. I estimated AR(1)-GARCH(1,1) model for series and record LLH. Then I apply any detection and correction method for outliers and correct some observatins that was detected by the method I apply. Now again I estimate AR(1)-GARCH(1,1) model for outliers adjusted series and record LLH again. Now I wants to apply Likelihood Ratio Test to check whether the outliers adjusted model is superior to the model of unadjsuted returns. I know how to calculate the LHR test but I am confused how to seltect the degree of fredoom for this test.
What is the degree of freedom in this case?


Regards,
Irfan Awan

[TomDoan]

If you are "correcting" the outliers by putting in dummies, then you have nested models and the degrees of freedom is the number of dummies. If you are doing something else, then a likelihood ratio test doesn't apply.

[irfanawan]

Dear Tom,
I just correct the outliers from the series then estimate the model again. The number of parameter to be estimated in both unadjusted and adjusted returns models remains the same. For example, AR(1)-GARCH(1,1) model. The number of parameters to estimate are 5. So for adjusted and unadjusted returns, the number of parameter remains the same. I just want to know through LHR test that the correction has improve the model or not. When I estimate the model for adjusted returns the LLH is greater than the LLH of model for unadjusted returns. So my aim to test The LLH are significant different from each other or not.

Regards,
Irfan Awan

[TomDoan]

The LR test is a test of models, not a test of data. If you change the data, the likelihoods aren't comparable and you can't do a formal test. If you have what you see as being bad data, explain to people why you changed it and what changing it accomplished.

[irfanawan]

Dear Tom,
Hi,

I estimated Multivariate GARCH model and wants to calculate portfolio weights and hedge ratios. the model is

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garch(p=1,q=1,model=varma,mv=bekk,pmethod=simplex,rvectors=rd,hmatrices=hh,piters=10,iters=500,asymmetric)

I use this formula to calcutae weights which is

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set  weight = (hh(t)(1,1)-hh(t)(1,2))/(hh(t)(2,2)-2*hh(t)(1,2)+hh(t)(1,1))

and hedge ratio

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set  hedge = hh(t)(1,2)/hh(t)(1,1)

the I use command "stat" to find the avaerge values of weights and hedge ratio.

In another program, I found formula for the weight and hedge as under

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compute [real] weight=(hh(t)(1,1)-hh(t)(1,2))/(hh(t)(2,2)-2*hh(t)(1,2)+hh(t)(1,1))

and hedge ratio

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compute [real] OHR=hh(t)(1,2)/hh(t)(1,1)

at the end they used

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display weight
display OHR

to get the value of weight and hedge ratio.

I estimate the hedge ratio and weights using both procedures but reached different values of weights and hedge ratio

Why the answers are different and what is exact formula for this ?

With high regards, Irfan

[TomDoan]

The Sadorsky paper has calculations of the weights and hedge ratios.

Unless I'm missing something,the two calculations you're giving are identical, but the first does the calculation for each entry while the second does only one.

[irfanawan]

Thanks Tom for your kind replies
Yes, Sadorsky used the latter formula to calculate the weights and hedge ratios and I used the following formula to calculate the weight and hedge ratios

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SET W_1 = %min(1,%max(0,((H(1)(1,1)-H(t)(1,2)/(H(t)(1,1)-2*COV_1_2+h(t)(1,1)))))
stat W_1

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SET HR1 = H(t)(1,2)/H(t)(1,1)
STAT HR1

Which one I should use for analysis?

Regards.

[TomDoan]

Your formula for the portfolio weights is wrong. You have H(1)(1,1) rather than H(t)(1,1) and the covariance isn't a fixed value---you need the time-varying GARCH estimate. Your hedge ratio is the same, so I'm not sure why you're asking about that. You should use the (corrected) formula from the Sadorsky paper for the weights.

[irfanawan]

Dear Tom
Thanks for your guidance.

I am asking you again and again because I am working on a project in which I have to estimate weight, hedge ratio and then a forecast of volatility as well. I want to forecast volatility using bivariate VAR-GARCH model of McAleer. I could not understand the command that is available in RATS. How can I forecast one step ahead using VAR-GARCH for two assets?

Thanks, Irfan

[TomDoan]

There is no closed-form solution for forecasting variance out-of-sample for CC (or DCC) models. Now one-step out isn't a problem because the one-step variance depends upon information from the sample. Are you doing rolling samples? If so, you can just do GARCH with the combination of METHOD=EVALUATE and INITIAL=%BETA (with your other options) after estimating the model through T using a sample through T+1 and let GARCH do the calculation for you. If you just want one step out of your actual sample, then you can just add some fake data from T+1 and do what I just suggested.

[irfanawan]

dear Tom,
Hello.

I want to compare the forecast performance of model using unadjusted and outliers returns series. I estimate VAR-MARCH with variance=VARMA. How can I get the forecast of 60 days? If not possible then what should I do to compare the performance? If I estimate the model like BEKK then what's the procedure the forecast variance of two assets? The formula, I did not how to apply this?


Regards, IRFAN

[TomDoan]

Compare the performance of the model doing what? Forecasting variances? What's the "actual" data against which you plan to compare the forecasts?

[irfanawan]

I want to compare the performance on the basis of forecast variance

Regarads