Adding external regressors on conditional variance model

Thank you very much for your prompt answer and help, Alexios.

I am running now some models and found some results that are puzzling me.

 From another thread I saw one recommendation that we should "(...) pass
values in the external regressor which are close in scale to the
variance equation", what makes sense to me...

However, I noticed that when I define the external regressors with
values close to the return series, the coefficients calculated for the
external regressors are non-significant, while I have a strong
hypothesis that those should be relevant in the process. Nevertheless, I
noticed that when scaling to an annual basis the external regressor
coefficients becomes significant...


Attached follow a sample code (sample_gjr_extregressor.R) and simplified
database (data.txt) with daily returns (r) and lagged realized variance
(lag_extreg) I am using as inputs for the models.

	
	

There are three models as below:

Model1: Standard GJR
Model2: GJR with lagged daily realized variance
Model3: GJR with lagged  realized variance annualized (scaled by 252)

The table below summarizes the results found.

	model 	omega 	alpha1 	beta1 	gamma1 	   delta1 	p-val_omega
p-val_alpha1 	p-val_beta1 	p-val_gamma1 	p-val_delta1 	LL 	For_01d

	Model1 	0.011449 	0.131705 	0.89924 	-0.08386 	   NA 	0.001217
0.000000 	0.000000 	0.000012 	0.000000 	-2033.96 	0.800619

	Model2 	0.011449 	0.131705 	0.899244 	-0.08387 	1.23E-08 	0.002944
0.000000 	0.000000 	0.000012 	0.999999 	-2033.96 	0.800635

	Model3 	0.004839 	0.066382 	0.69109 	-0.08387 	0.001161 	0.633308
0.037429 	0.000000 	0.010968 	0.000451 	-2012.57 	0.778901


Any idea or suggestion on what might be happening?

Thanks again in advance for any help with that issue.

Best Regards,
Assis.



2015-08-20 11:01 GMT-03:00 alexios <alexios at 4dscape.com
<mailto:alexios at 4dscape.com>>:

    Hi,

    The answer is yes and yes. Add variable(s) lagged.

    Best,

    Alexios


    On 20/08/2015 14:57, Assis Duraes wrote:

        Hi,

        first of all I would like to thanks for the rugarch package. it
        is really
        useful and a very nice package.

        I am investigating the effect of external variables on
        conditional variance
        models forecasts. more specifically, I am would like to check if the
        addition of implied volatility and realized variance as external
        regressors
        on a GJR (1,1) model somehow enhance the daily volatility
        forecasts of it.

        Looking for a tool to help modelling it I found the rugarch
        package, and
        started looking into it. In fact, at this point, I believe I
        have a very
        basic question. but did not find an answer on previous posts or
        in the
        package documentation.

        Should I inform the external regressors matrix in model spec
        already lagged
        or not? I imagine, yes, since I did not find in any place where
        specify the
        lags for those regressors, but would like to confirm. In case
        affirmative,
        If I want to use a same variable with different lags I need to
        inform it
        multiple times, obviously with different lags, in
        external.regressors
        matrix, correct?

        My apologies in advance if it is explained somewhere, but as I
        explained, i
        search without much success..

        Thanks in advance for any help with that,
        Assis.

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