Financial professional with expertise in financial modeling, risk management, and related quantitative methods including Monte Carlo simulation, linear and logit regression, and statistical hypotheses testing. For past few years have been engaged in developing econometrics models related to Stress testing for a large financial institution.

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accepted When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
16h
comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Richard, I saw your answer and comment. And, I am not sure if I understand them. That's because if the variance is unobservable and is replaced by the proxy Residual^2... then on the righthand side of the equation, both the ARCH term = GARCH terms which does not sound right.
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comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Richard, I'll read the article. But, if you find it difficult, I most probably will find it obtuse. So, how does GARCH structures the dependent variable? I thought I read somewhere that it does simply take Residual^2 as a proxy for the residual's variance. But, does that sound right to you?
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awarded Informed
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awarded Autobiographer
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comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Actually, this is a piece of the GARCH(1,1) model I really don't understand. What is the dependent variable? It is the variance of Y. But, how do you calculate it for every single observations within the learning sample?
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comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Richard, I give you +1 not only for a very good answer but also some excellent comments. Anyone, before contributing on this issue is encouraged to read Richard's comments first. I am not giving points for an answer that Richard has already fully addressed in the comment section.
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comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Richard, you understand my model framework precisely. Just a couple of details. All the original regressors have positive reg. coefficients within the original regression or Mean Equation of GARCH. Out of four exogenous regressors (in my original model, not the example) only one is stat. significant. The ARCH term is not sign. and has flipped signs within the GARCH(1,1) + exogenous variables. In the GARCH(1,1) the ARCH term is positive but not stat. sign. The GARCH term is not stat sign. in GARCH (1,1). But, it is in GARCH(1,1) + ex. variables.
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comment Is it ok to have a unit root within an independent variable?
Cagdas and Richard, excellent comments. Thanks much. I have up-flagged them all. Cagdas, I have no experience with Cointegration models; but, intuitively I so agree with you. They seem to me like unicorns. I can't see how two "level" variables could possibly have a difference between them that is stationary for long enough to build a model with. Your State Space model is intriguing. I'll have to study that. Richard my econometric model example was just that, facilitate our conversation. I am not suggesting there is any theory behind it suggesting they could be cointegrated.
Mar
27
comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Richard, I am working on a company proprietary model so I can't share the specifics. I'll use an example that replicates the situation. GNP ~ S&P500 + Housing price. So, when I run a GARCH model (using EViews)... I first run it using only the ARCH and GARCH terms. And, neither is statistically significant within the Variance Equation. I run the GARCH model a second time, with the two independent variables. Now, the GARCH term is very stat. significant and so is of the ind. variable. What do you conclude in this situation?
Mar
27
comment Is it ok to have a unit root within an independent variable?
Richard, we can make any hypothetical examples which would work just fine. Let's say your have a model: GNP ~ S&P500 + Housing price + 10 Yr. Treasury rates. If you take all those variables on a nominal level basis, they all have huge Unit roots. Three of them trend upward forever (GNP, S&P500, Housing price). You could detrend them all by looking at periodic % change (from one quarter to the next) and avoid the Unit root issue. But, maybe you could keep them on a nominal basis (Cointegration framework). I don't know.
Mar
27
comment When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Your comment makes perfect sense to me. Is the heteroskedasticity associated with the level of the fitted value or estimated value? Or do you want to go more granular and check whether the heteroskedasticity is associated with a particular independent variable(s). In my mind, your comment qualifies as a good answer. I would give it thumbs up. You are welcome to structure it as such.
Mar
27
asked When testing autoregressive conditional heteroskedasticity with GARCH do you need to include the ind. variables?
Mar
27
comment Is it ok to have a unit root within an independent variable?
Cagdas, is that in essence what a Cointegration model is? Thus, within this framework the non-stationary trend of the dependent and at least one independent variable have to match closely. If you have a mismatch, you have a problem.
Mar
26
asked Is it ok to have a unit root within an independent variable?
Mar
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comment How to describe statistics in one sentence?
An observer visiting this site would derive that my answer is the worst one... even worse than someone who made a joke about the question. The very best answers invariably just state statistics are just methods to better understand data. However, the latter do not tell you much if anything about the field of statistics. That's especially true if you were to address such answers to outsiders. On the other hand, my answer states something precise and descriptive about the field that is readily comprehensible by outsiders. That should count for something.
Mar
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comment How to describe statistics in one sentence?
In each of those cases, the answer to those questions has a strong element of statistical significance and whether what you are looking at in any shape or form is different vs. what could occur by sheer randomness. To most of us a negative vote means an explicitly wrong answer. I don't see how my answer could be categorized as such.
Mar
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awarded Popular Question
Mar
6
comment How to describe statistics in one sentence?
I see it differently. Ultimately, whether you are conducting hypothesis testing, regression modeling, or any other estimation you most always measure whether the difference between your estimate vs a naïve model, or difference in observations are statistically significant or not. My sentence captures the essence of statistical significance vs. randomness. If others agree, can you give me some up votes, so my comment that is easily justifiable is not treated as a plain wrong answer just because of one individual's subjective interpretation of narrowness.
Mar
5
answered How to describe statistics in one sentence?
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