Elan.... I know you are one of the long timers here and I would really like to respect that.

:) This is a bit silly!

First let me agree on something you mentioned -"In other words, the slope of the index was negative for two weeks "
Yes this would be correct - Except on a time series it all depends on the periodicity.

Slope is not patented to BC ... Its a mathematical concept which you first learn in Middle School geometry and then in Introductory Calculus.

Its simply the instantaneous rate of change - key is the time period.


"BEFORE the day on which you claim that its slope changed" : I did not make any such claim.

But I have a pretty good understanding of the concept to know that - there has to be a threshold in point in time ie comparison of the 2 derivatives to make this
call.

Ie Prior Slope ( lets call that Slope 1) Calculated between Time point T and T-N compared to a Shorter time Slope(Slope2) Lets say time point T to T-K where N>>K.

TEST : Slope 1> Slope2

Even better would be something like this Slope 2 = Slope between Time points T and T-K and Slope 1= Slope from T-K-1 to T-N in which case they are mutually exclusive.
In this setup you choose K and N ie they are your parameters.

Simple-speak example: Both K and N=1 then in my 2nd setup

Slope2 = Todays Change in price ie 1 day slope
Slope1 = Yesterday's change in price T-1 slope
if the directions dont match - Slope has changed. Mathematical fact.

Utility = ZERO! because this is literally Random Walk.

Everything ie BC approaches are about calling a "definitive" change in Slope ie direction of the curve - in this case the Economic Time Series called Stock Index( that is the mathematical definition) you can define it whichever way you want - that would be your indicator. BCII simply uses a Smoothed proxy of a Long term Price average and calculates the slope of that to make the call on the primary series.


I dont think I can get you on the same page - but I am making perfect sense and crystal clear.

All the best and I have always enjoyed your posts!

Best
Anindua