Subject: response re which series

From: Upmanu Lall <[email-masked]>
Date: Mon, 18 Jan 1999 17:24:32 -0700

Hi Bonnie
1) First please be sure to mail me at [email-masked], our
pub.uwrl.usu.edu workstation is acting up
2) I'll be in Las Vegas T through H for a meeting
3) here are some thoughts

Given your experience with all these methods and series, and the lack of an
obvious solution to whether the PC, the aggregate, the clustered or the
individual series are likely to work better, I have the following thoughts
that I would like reactions on.

1) The competing representations are a time series or a "regression" on
last step approach
2) We can condition on existing P,T+N or just N, or just P or T. It is
unclear whether long lags are needed if N info is being provided, since
presumably the N info is the long range state predictor.
3) So far you have focused largely on a multivariate representation,
although some univariate work was also done. We anticipate some problems
because of datra limitations for the multivariate setting. These have
probably been manifest.  Regarding the univariate case, there is still the
issue of whether the N info and/or the P/T info is useful for forecastin
T/P.
4) it occurs to me that at least we ought to boil down a framework in which
the investigation can proceed systematically in the univariate case before
much more additional energy is expended.

In the spirit of 4) here is a proposal.
First cut we could identify up to 3-5 predictors of the seasonal P or T
using just a partial correlation analysis with past P, T, N and/or NAO, PDO
etc.  If we want to consider nonlinearity then let's consider the following

We need a simple yet reasonably robust procedure for deciding what is
likely to be predictable and using which variables. We are data poor so
getting too creative with nonlinear methods, a la Mut Inf, may not be
productive.

In this setting, let's consider this as a conditional prediction problem
where we work with a simple categorical predictor much like the NOAA crowd
does

Say P is to be forecast at time resolution (season, month) tau, and lead
time lam (e.g., 2 seasons)
Consider P to be discretized into 3 categories (i.e., at the 33 and 66
percentiles) as below av, average and above av
Now let's consider as predictors P_t-2, N_t-2, PDO_t-2, T_t-2, P_t-3, N_t-3 etc

(note - Dan Ames finds that the correlations for Yakima Apr-may-june flow
are high with SST in  Oct Nov, but lower DJF - peculiar but robust - so it
may be good to look at different lags of N, PDO etc)

Let's divide each predictor into 3 categories also.

Now let's evaluate the  joint prob tables (3x3) for each predictor
this is an estimate of f(x,y)
so we could compute an M. I. like measure as
sum log(f(x,y))

(f(x) and f(y) are identically 1/3)
and choose the predictor that has the highest MI - there is also the issue
of significance I suppose
can we get the answer to that from known properties of a multinomial
distribution ?

Next we consider forming the same statistic but as a partial MI,
conditioning P_t on P_t-2 and adding on N_t-2 etc
Now we'll have 3 categories for each 1s t predictor category etc and the
same evaluation

Perhaps this is as far as we can reliably go.

This is much like what would happen with the MI calculation, but has the
advantage of being much faster and also giving the "forecast" model as a
byproduct.

I am proposing that we use this quick screening tool to assess wheter the
regional series, the cluster series, or the aggregate series can be better
forecast

I presume that the regional series are highly correlated with each other -
particularly within a cluster.
Seems to me that this may give an opportunity for validating the forecast
for one region by applying that model directly at the other region within
the cluster. This could be done in addition to or in place of the leave x
out forecasts.

The forecast could then be assessed by the percentage of hits in the right
category similar to what you were already doing.

There is also the opportunity to use the PC's of a potential predictor
matirx as predictors in this mode and decide how many we need to use.

I have jsut started thinking about this retrograde technology --- from MARS
and projection pursuit back to categorical. May be thi s is what we need to
step back to for a bit.

Incidentally, did you ever try forecasting using jsut a time series of the
ranks of P, rather than the actual values ?

Sorry if this email was incomprehensible. I may be able to call tomorrow
afternoon
Balaji - any ideas/thoughts ? Piechota - Dracup were working with
categorical things - any ideas based on your critique of that work ?

___________________________________________________________________
Upmanu Lall
Professor, Civil and Environmental Engineering
Associate Director, Utah Water Research Laboratory
Utah State University
Logan UT 84322-8200
___________________________________________________________________
e-mail:  [email-masked]
Web: Personal: http://grumpy.usu.edu/~FALALL/ulall.html
Research Group: http://pub.uwrl.usu.edu/~ulall/
Institutional: http://www.engineering.usu.edu/uwrl/www/faculty/lall.html
___________________________________________________________________
Phone: 435-797-3184                               FAX: 435-797-3663
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