.
In week seven, we'll finish our discussion
of estimation theory with a practical
problem of estimating the value at risk in
the constant expected return model.
One of the things that we'll concentrate
on is computing a standard error for value
at risk to show how accurate value at risk
is.
And we'll see that it's, it's actually
quite difficult to get an analytic formula
for the standard error.
This will serve as a motivation for
learning about the bootstrap which is a
computer simulation technique that we can
use to let the computer compute standard
errors for estimates instead of using
mathematics, you know, to derive
analytically what these things are.
So, we'll do a review of the bootstrap and
show how it's related to Monte Carlo's
simulation, and then we'll apply for
bootstrap for computing standard errors
for all of our estimators of the
parameters of the constant expected return
model.
After estimation theory, then we'll move
into the last topic in review of
statistics and this is hypothesis testing.
We'll see that once we have an estimated
model we often would like to test
hypothesis about the model and these
hypothesis could be about,
You know, values of the parameters of the
model, for example.
You know, is the mean zero or is the
volatility greater than ten%?
And some hypotheses are about verifying or
refuting the assumptions of the model. For
example.
Are the returns actually normally
distributed?
So we'll do a review of hypothesis
testing, the various concepts of setting
up hypothesis tests and the alternative.
and a discussion of what test statistics
are.
And then, we'll do applications of
hypothesis tests to the constant expected
return model.
We'll look at hypothesis for particular
coefficient values, you know, could be
testing whether the mean is equal to zero,
or the mean of one asset return is equal
to another asset return.
We'll also look at test of hypothesis of
the distribution of acid returns.
And in particular, we'll look at the
hypothesis of whether or not returns are
normally distributed or not.
And then, we'll also look at hypothesis
for the assumptions that the returns are
not auto correlated over time.
So we'll have a hypothesis test for no
auto correlation.
And then, finally, we'll end our
hypothesis testing by looking at the
hypothesis that the parameters are
constant over time.
And here, we'll make use of rolling
statistics.
We'll look at, like, things like rolling
means, and rolling variances, and rolling
correlations, and we'll use these rolling
estimates to determine whether or not the
hypothesis that parameters are constant,
you know, is validated by the data.