Not exactly an Excel question, but I am hoping some kind soul will
share his/her knowledge in this area.

I'll ask my question by example. The problem is much more general,
involving over 20,000 data points.

When I look at the DJIA closing indexes from Sep through Nov 2008, I
see the following trends. 9/2 thru 10/1: shallow downward slope;
10/1 thru 10/10: steep downward slope; 10/10 thru 10/27: shallow
downward slope [1]; 10/27 thru 11/4: upward slope; and 11/4 thru
11/21: downward slope.

Is there an algorithm that would recognize those trends?

What I had hoped might work is a "moving SLOPE" algorithm. That is,
for each date, calculate the slope of the N days ending on that date,
and recognize trends by counting the sequence with the same sign [2].

As you might imagine, that did not work. First, the change in the
sign of the SLOPE trails the points of inflection that I observe
empirically. Second, I found myself fudging N to get something close
to what I observed for __that__ sample data. I am uncomfortable doing
that; but then again, I don't know what N would be reasonable.

Before I started working with a "moving SLOPE", I did try simpler
things, none of which worked satisfactorily.

The simplest approach is a "moving N-day yield" -- that is, y[i-N]/y
[i] - 1 -- and again, counting the sequence with the same sign. That
has many anomalies, of course.

Another approach that I considered but have not tried yet: applying
either of those two approaches to an N-day moving average of DJIA
indexes. But again, I think the "moving SLOPE" approach will trial
the inflection points that we observe empirically.

I am not above (or below?) developing VBA code to do this. But I'm
still at loss to figure out a general algorithm, one that makes sense
theoretically, not just tailored to the sample data and hope for the
best.

Any thoughts?


Endnotes:

[1] Actually, I perceive a horizontal slope from 10/10 thru 10/22, and
a downward slope from 10/20 thru 10/27.

[2] I would probably recognize horizontal trends by some range check
on the slope as a percentage of the data. But I never got that far
along.