John Dodson:hi Peter
  Peter:Hi John.
  Jingnan:Hello John, Can I ask a question?
  John Dodson:Sure
  Jingnan:In your handout, in Scaling expectation, it seems E[Y_T+i|F_T]=m_T+1,
I got a little confusing.
  Jingnan:I thought each E is different
  John Dodson:Jingnan, yes each $m_t$ could be different, but we do not have a
model for that
  John Dodson:so we usually set all $m_t$ to the same value, such as zero
  John Dodson:if we have a timeseries for the "borrow" rates, we could use that
instead
  Jingnan:So here you set each E[Y_i | F] equales to same value of m_T+1,
right?
  John Dodson:yes, in general $E[Y_t|F_]=m_t$ for each $t$ in our historical
sample. We set them all to the same value unless we have a good reason to do
something more precise.
  John Dodson:we do this so that the conditional expectatons
$E[\epsiolon_t|F_]$ are all zero
  Jingnan:And in Variance Targeting, when we get this formula for w, substitute
\sigma for \hat\sigma, are you expecting us to plug in MLE to got other three
parameters?
  John Dodson:Yes, set-up a likelihood maximization optimization to find
$\hat\alpha$, $\hat\beta$, and $\hat\gamma$.
  sangya:John, are there constraints on the parameters? do they equal 1?
  John Dodson:Sangya, the most important constraint is that $h_t$ should never
be negative. So generally this means $\omega\ge 0$, $\alpha\ge 0$, and
$\beta\ge 0$
  sangya:ok!
  Jingnan:Is there any difference we directly calculate parameters from MLE and
plug in variance targeting formula to get them?
  John Dodson:Also, since $\sigma^2$, the unconditional variance, cannot be
negative, you also have $\alpha(1+\gamma^2)+\beta<1$
  Jingnan:Is there any difference we directly calculate parameters from MLE and
plug in variance targeting formula to get them?
  John Dodson:Jingnan, you will get (slightly) different values, but they will
probably be fine. The advantage with variance targetting is that the numerical
optimization is a little easier.
  Jingnan:When deducing the formula, does it also assume h_t is uncorrelated
with e_t?
  John Dodson:Yes, I think this can be proved.
  Jingnan:Thanks !~
  John Dodson:Assuming $\epsilon_t$ and $\epsilon_$ are independent
  John Dodson:I should be on campus by about 2:30 on Wednesday. If anybody
would like to meet me before the session, let me know.
  Mo:Hi John, i tryied to use (garchset and garchfit ) matlab for the modeling.
im getting some error.  How can i get it start in matlab?
  John Dodson:Sorry, Mo. I don't know much about MATLAB's packages. There is
probably a way to set it up for this specification, but you will have to review
the documentation or get some technical assistance.
  John Dodson:Which package are you using, but that way?
  Mo:the mathwoks specifies econometrics but i do not have it and tryied to use
the function handle in the command. That s where i got errors msg.
  John Dodson:I do not mind you using packages, but I cannot support them. You
should be able to do the problem with the standard functions.
  Sharon Linden:When you get a chance John, I am getting values for alpha,
beta, and gamma but am unsure how to judge their accuracy. If
$\alpha(1+\gamma^2)+\beta<1$ holds would you consider that a good indication?
  John Dodson:Sharon, a good way to check if you have reasonable values is to
change the initialization values for the numerical optimization and see if you
come to the same results. Generally $\beta$ will be close to one and $\alpha$
will be close to zero.
  John Dodson:Any questions?
  Greg:I have a question from a couple of weeks ago...
  John Dodson:Sure, Greg. What's that?
  Greg:Oct 5 slides.  Slide 11.  I couldn't follow how to find I_X.  How do you
take the derivative WRT theta prime?  How do you take the covariance of that?
  John Dodson:this is just a gradient. Usually, if $\theta$ is a column vector
and f is a scalar, then $df/d\theta$ is a row vector. so conventionally
$df/d\theta'$ is a column vector
  Greg 2:Thank you, that helps.  Is X a vector?  Then we end up with an Nx2
matrix.  And that is what we take the covariance of?
  John Dodson:yes, $X$ is a vector, but $\log f_X(X)$ is a scalar. So you are
evaluating the covariance of a vector.
  John Dodson:or equivalently the (negative) expected value of the Hessian
  Greg 2:That's part of what threw me... I've never taken the covariance of a
vector before.
  John Dodson:I think you have. All covariances involve vectors. The covariance
of a scalar is just a variance.
  Greg 2:Well, I'll have to puzzle over that for a bit.  I'm used to finding
the covariance between two or more timeseries, so I'll need to think about what
this all means conceptually.  I won't keep you late, though.  Thanks for your
help tonight.
  John Dodson:Sure. Unless someone else has a topic, I will let you go
shortly...
  John Dodson:I will post the log.
  Greg 2:Take care.
  scott:Thanks John.  Have a good night.