A question on 'statistical analysis' of a time series

["Nicholas Kormanik" <nkormanik@xxxxxxxxxx>]

I'm wrestling with an issue that perhaps some here might like to comment on
(Steve, Walter, Ton, Guy??), or perhaps steer me to an individual (somewhere
in the world) that might be able to shed light.

As *one* example (and as you will recognize, there are thousands similar),
I'm attempting to study the functional relationship:

       3-day ROC of typical price at time t+3 = function of ( 13-day
Stochastics RSI ) at time t

I'm initially looking for a 'significance' test.  The 'hypothesis' is that,
yes, based on the data analyzed, there *is* a statistically significant
functional form there.  The 'alternative hypothesis' is that, no,
unfortunately and sadly, no statistically significant relationship exists
between these two variables.

Sounds fun, huh?

Actually, it's not fun.

'Visual analysis' and 'intuitive understanding' seems sort of plausible to
many of us --- when we see the StochRSI starting to head up, we generally
expect that the ROC will be heading up.

But I am after 'statistical' understanding.  And getting this seems
surprisingly difficult.  For starters, attempting to use 'linear regression'
seems of no use --- a) we surely don't have linear relationships in this
example; b) we in fact have an *oscillator* that goes up and down and up and
down; c) a particular level of StochRSI and its expected relationship with
ROC will depend on whether StochRSI is heading up, or heading down, thus we
would appear to need at least a *third* variable, perhaps a dummy variable,
heading up=1, heading down=0 (and classifying these will not be all that
clear cut); etc.

Getting a flavor of the problem?

If you have any insights, please post 'em.

Thanks,
Nicholas Kormanik