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nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-10 14:36
I see pattern. Mostly it can be defined simplistically as a P1=(X > A) & (Y < B) and such conditions are set like this (flavor of idea).

P1=(X1 > A) & (Y1 < B)
P2=(X2 < D) & (Y2 > C)
..
Pt=(Xt < S) & (Yt > T)

Basically, it is a cut through the space of path realization.

let P = {P1,P2,...,Pt}

Question, how should I define dP, i.e. differential?

I am struggling to formulate it. Head against Wall

Maybe some educated guys from "differential geometry" can suggest simplified definition? (Disclaimer: "Diff.geom." is just a sound for me)

PS. It is a pattern I see in data and it is not a solution of optimal control (maybe it is the same, but then, please, explain).

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

silverside


Total Posts: 1444
Joined: Jun 2004
 
Posted: 2021-02-10 17:25
it sounds very like a copula ?

http://www.columbia.edu/~mh2078/QRM/Copulas.pdf , for example of an introduction.
The copula allows separating the "strength" of the relationship (the correlation) from the "shape" of the relationship (Gaussian, T, Humbel etc) which mainly affects how the tail scenarios interact.

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-10 21:40
@silverside

Actually, not like copula, but trying to understand what do you mean I came to this:

If to start with discrete time, e.g. t=1,2,3 and I have pattern like Up, Down, Up (UDU) out of all 2^3=8 combinations (=UUU, UUD, ...), then I have to fold path with single states into 8Dim state path, just like we do it for Markov Chains. So, yes, then in this case 8Dim Copula applies. Is it what you meant?
Thanks.

PS. I read this note long ago (~2016 is already long ago...!). Good one.

PSS. In my example, space is larger : 4x4x4=64. Sorry, miscalculation. Problem is solved a bit differently.

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

ronin


Total Posts: 683
Joined: May 2006
 
Posted: 2021-02-11 10:01
> I am struggling to formulate it.

And I am struggling to understand it. You have two assets, and you want the probabilty of them both staying above their respective barriers, where the barriers change with time? Or below? How do change here - they seem to be a bit random?

It's not a copula - the correlation doesn't make any difference. It's just two independent barriers.

But I don't understand what you are counting there. Is it the number of hits, is it the time of the first hit, is the probability of a hit before some time?

"There is a SIX am?" -- Arthur

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-11 10:35
I defined the pattern as entire chain Pt, where, for example, I observe over 5 periods of time something like:
- DUUDD for one asset or
- for two assets it looks like (DU)(DD)(UD)(DD)(UU)

I simply mapped these combinations to numbers, parse it through data, and update array of counters (sort of historgram) if i_pattern is found. Wanted patterns rise like bamboo. Supersonic fast.
At the end decode patterns with highest count into my set of {(DD),(DU),(UD),(UU)}.

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

ronin


Total Posts: 683
Joined: May 2006
 
Posted: 2021-02-11 10:49
Ok, that's a bit different than what I thought.

I think we had a thread about wavelets, didn't we? Because that's what this is.

But I wouldn't go there if I were you. That's just voodoo. Search long enough and you'll find all sorts of patterns, all with zero predictive value.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-11 10:57
I know/heard about wavelets and do not spend time on that.

Do you suggest that my idea to search patterns is flawed? Why?

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

ronin


Total Posts: 683
Joined: May 2006
 
Posted: 2021-02-11 11:15
Unless there is a good reason for a pattern, it's just a random fluke.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-11 11:42
Well, I see "good" lead-lag correlogram. It led me to think about certain behavior which follows patterns. My pattern-counter technique confirms my thought.
Of course, presence of a pattern does not guarantee a win. It must coincide with other signals.

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

deeds


Total Posts: 516
Joined: Dec 2008
 
Posted: 2021-02-11 15:50
Pattern probabilities seem to often vanish in the noise, after truing up for structural limitations and being precise.

Three leads on unmined territory wrt pattern probability structure, not exactly on point, hence unmined
- Ulf Grenander
- Persi Diaconis / Bernd Strumfels, etc
- Judea Pearl

this will/is lead(ing) somewhere. (i hear the echo of a jslade comment from the future) The intermediary is RMT (per other thread) and representation theory. I note that a fake Economics Nobel was recently awarded to a practitioner in another room in this theoretical house around Tropical Varieties (not kidding!)...all floating in the googlesphere...(thank you to the great Abundance for posting Diaconis' monograph on probabilities on groups...it's probably way too elementary and distant from econometrics/data orientation for the appetite of most...but look at Diaconis other work and how he thinks...)

Another stray thought - financial option structuring/payoff decomposition with risk neutral framework around options on quantiles. A few authors hit this hard for a decade.

EDIT: and just straight messing around with barriers as Peter Carr and crew do with their analysis of Lookbacks...Carr's sequential exchange may be relevant

EDIT: (to be precise...i wouldn't expect jslade to agree with my cheerful outlook for this line of exploration)


chiral3
Founding Member

Total Posts: 5221
Joined: Mar 2004
 
Posted: 2021-02-11 16:02
"Three leads on unmined territory wrt pattern probability structure, not exactly on point, hence unmined
- Ulf Grenander
..."

Not sure if you can make it connect to OP but Mumford picked up the baton nicely on this. His book is very concrete.

Nonius is Satoshi Nakamoto. 物の哀れ

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-11 16:30
@chiral3

https://arxiv.org/abs/math/0212400

Aside: it crosses with ideas formulated by my favorite S.Lem in his (also my favorite) book "Philosophy of Random" (~1970), where he tries to define "genius piece of Art". He tells that such piece must be a golden balance between concrete/specific and vague/random, such that the brain of spectator generates images and patterns by traveling through the structure of the piece. He says that it must be specific enough to show the structure and vague enough to stimulate imagination (by Leonardo as "searching camel in the clouds"). It also links to the art of technical trading, where traders are taught to buy after "Head and Shoulders" pattern is formed (Camel is found, let's sell it!). No, I am not after this kind of things.

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

chiral3
Founding Member

Total Posts: 5221
Joined: Mar 2004
 
Posted: 2021-02-11 16:35
Ooof, that abstract sounds foofy. The book is fairly concrete.

Nonius is Satoshi Nakamoto. 物の哀れ

deeds


Total Posts: 516
Joined: Dec 2008
 
Posted: 2021-02-11 19:10
c
@chiral3 - Mumford is an absolutely awesome call, and in places very cleverly data driven...did some time in neurophysiology (single cell and networks) and his work is rigorous in many places...would comment everyone who gets a reputation goes mad and speculates beyond their bailiwick (watson, pribram, etc...)

EDIT: @c3 - really right on with the algebraic geometry slant from Mumford's early work...that's a third of the territory i have in mind

chiral3
Founding Member

Total Posts: 5221
Joined: Mar 2004
 
Posted: 2021-02-13 05:54
Is Singer RIP.

Nonius is Satoshi Nakamoto. 物の哀れ

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-14 12:01
c3 / deeds / ronin / silverside

thank you!
discussion was great. helped a lot.

As I said - copula idea is wrong path.
My original pattern idea transformed into something different, like "feature extraction", but with some angle.

@c3

Sorry for my outburst about artistic patterns - this is long story, sort of "free time philosophizing", I have to write it down systematically, but have no good habit about writing.

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)

chiral3
Founding Member

Total Posts: 5221
Joined: Mar 2004
 
Posted: 2021-02-14 15:02
No worries. I actually still don't understand your original question! Rare that someone brings up Ulf and the Brown crew, though.

Nonius is Satoshi Nakamoto. 物の哀れ

nikol


Total Posts: 1366
Joined: Jun 2005
 
Posted: 2021-02-14 16:54
"still don't understand your original question"

See discussion with ronin about "(DU)(DD)(UD)(DD)(UU)"-chain.
Started reading Mumford. Rich content. Thank you for ref.

... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c)
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