Esoteric Knowledge of Pivot Points Statistics

[w76sammy]

As I have explored the topic of support and resistance I have taken interest in a specific kind of S & R levels, pivot points. I have read a couple different articles that show a statistically derived probability that a certain pivot point will be touched or some behavior will occur in relation to the various s & r levels. Take for example Jamie Saettele’s article in Investopedia. (Ref. 1)

The result: there have been 2,026 trading days since the inception of the euro as of October 12, 2006.
• The actual low has been lower than S1 892 times, or 44% of the time
• The actual high has been higher than R1 853 times, or 42% of the time
• The actual low has been lower than S2 342 times, or 17% of the time
• The actual high has been higher than R2 354 times, or 17% of the time
• The actual low has been lower than S3 63 times, or 3% of the time
• The actual high has been higher than R3 52 times, or 3% of the time​

I have degrees in engineering and physics:cheesy:, so I prefer empirical proof over “take my word for it”. The issue I’m having is that my statistics are a little rusty! How are these probabilities calculated? I mean how is the data statistically analyzed to come up with 44% of the time the low has been lower than s1 (see the first bullet above)?

It seems reasonable, given the history of pivot points, there should be examples on how to do a hypothesis test or make a probability distribution of price action as related to these levels. Or is this just esoteric knowledge?

CAN ANYONE HELP???:?:


Ref. 1: Using Pivot Points In Forex Trading;

 

[Shakone]

How are they calculated? Say for one year, you take all the trading days (perhaps 260 if we include all bank holidays). The R1, S1 etc can be calculated from the previous day's Hi Lo Open Close, for each of those 260 days. You then find that for example the daily low was lower than S1 114 times out of those 260 and you get 44% approx. Of course you can do this for more than just this year. Not that hard to do. But it doesn't tell you a great deal about WHAT to do.

 

[w76sammy]

I’ve done as you suggested, about a month ago. My Excel spreadsheet has over 8,000 data point and after coding algorithms(very simple algorithms) for pivot points etc it tends to crash excel! I’ve had to move analysis between multiple spreadsheets and I am now doing cals in R using R Commander.

I agree, it says nothing on what to do. Going forward from say r1 to r2 I’ve repeated the process. So if I find that for a given period (say 3 months) I have a 39% chance of reaching r1 and using the same method I find that I have 20% chance of reaching r2, what is the probability that I will reach r2 if price action is at r1? Would I just multiply the two percentages to made this assessment or maybe divide? So, .39 * .20 = .078 (Seems Low)?

 

[Shakone]

Probability that it hits R2 given that it hits R1, should be the probability of it hitting R2 divided by the probability of it hitting R1, so about 0.51 in your example.

 

[w76sammy]

Hey that is awesome. Thanks for the input; I sure like .51 better than .078! Do you think you could point me in the right direction on the basis for your calculation or rational for division as opposed to multiplication?

I think I will try to prove this with data. I’ll also try to post some pictures or a spreadsheet with results.

 

[Shakone]

Conditional probability of an event B given another event A is written P(B|A) . In your case B='hitting R2', A='hitting R1'

There's a formula for calculating this (Bayes' theorem, easy to wiki or google)

P(B|A)=P(B and A)/P(A)

in the case you mention, if it has gone above R2, then it has also gone above R1, so B and A is really just B

So
P(hitting R2| hitting R1)=P(hitting R2 AND hitting R1)/P(hitting R1)= P(hitting R2)/P(hitting R1)=0.2/0.31