[R-sig-finance] Fwd: negative weights

[Gabor Grothendieck]

On 4/29/06, BBands <bbands at gmail.com> wrote:
> On 4/28/06, Dirk Eddelbuettel <edd at debian.org> wrote:
> >
> > Hm, you didn't mention forecasting. I am not even sure where weights would
> > enter there...
>
> On 4/29/06, Patrick Burns <patrick at burns-stat.com> wrote:
>
> > I'm not sure what you are aiming at.  I would think
> > that a negative weight would mean that the bigger
> > the residual for that observation, the better.
>
> I build these models to forecast future returns, but maybe I am
> barking up the wrong tree on this one. Let's use a very widely
> accepted meme to see:
>
> Suppose you buy into the Columbine thesis that mean reversion prevails
> in the short term while momentum prevails in the long term. Let's look
> at the simplest model that can capture that thesis, a
> two-period-return model where a is the long-term return and b is the
> short-term return. In order for this model to work you would need
> weights of something like 1 and -1 for a and b respectively. Now
> expand the model to a reasonable number of returns and a larger number
> of securities and a regression using a shaped set of weights including
> negative weights starts to look like an attractive idea. Of course I
> can preprocess the data and then feed it to the model...
>
> Any ideas?

I think you will need to specify your model more concretely to get more
than passing comments.  At any rate, note that if the weights can be
negative then the sum of squares to be optimized is no longer a convex function
of the coefficients so we really don't have a conventional least squares
model and uniqueness and existence have possibly different answers.