Quote from raker:
I wonder if Maestro could help answer a problem in regards to the centre of gravity or central tendancy of a data set , which one is a better measure or are they all valid ?
There are a few ways to measure the centre of a data set from which the standard deviation can be caluated .
1. Using the basic mean(average) of the data set.
2. A Linear regresion line can be used which is basically a least squared average of the data set.
3. The midpoint of the data set or median or the difference between the high and low for that time of day.
There are others but each are a valid measure of the centre or average of the data set and each will give a different standard deviation calculation.
I used your example(Maestro) from a previous thread where you pointed out about making the time series more gausian or normally distributed by calculating the 30 day average true range of the series and then putting a 30 day long linear regresion line on it and then measure the deviations from it.
I myself have along those lines have tried to normalize and create more normally distributed data by experimenting with intraday data with different time series such as a basket of stocks above and below the current day open and then normalizing the data into a percentage and then looking at the 10 20 and 30 day average ranges of the data set for a particular time of day (like a vwap but withot the volume)
I have created "variable period regresion lines" and "mean averages" and "midpoint of the day" of the timeseries and calculated the deviations from it.
It seems from just an emperical observation (not statistically tested) that the analogy of mass behavior or the flock of birds changing direction and the metronome example where they all start moving in sync with each other happens in the stock indexes intraday such as the dow 30 and the S&p 500 when there is a confluence of the timeseries when price is hitting the standard deviation created by the regresion line as well as the deviation created by the mean and the midpoint when all these different central tendancies hit their deviations at the same time , it seems to create meanful or large reversions , its as if all the algorithms that are used for trading stocks for the buy and sell side part of the institutions all see the same benchmark and act in unison to create a kind of "hearding affect of computer models"
Here is something that is rather old.
It is called the "pinwheel".
It was invented as a leading indicator of trending price movement.
There is always a triangular location that serves as an arbitrary pivotpoint for the "herd".
I used 10, 20 and 40 periods as the length of MLR's which were fitted to charts. The MLR's always end on the Present and, visually, anyone can observe trend changes very easily and in a timely manner. The pinwheel was put into the wealthlab library when the library was invented.
What is nice about the pinwheel is that it is simple and lets a person make a lot of money as time passes. What shows up promptly is how human perception works and it does lead a person to catch on to how the market follows an order of events.
You can think of a school of fish and understand how the shcool reacts to various sizes of predicators. I use porposes, sharks and whales relative to their common food supplies fishwise.
The neatest trigger signals come from the relative angular velocity set. The area of the triangle is a keen thing too. At one time I was reading hand plotted real time overlapped (15 min) 30 min charts and projecting their adjacent bar slopes as two sets to keep a "zone" of near future price banded. I felt that having leading banding was a good idea at that time. It had to be done manually since there was no real time plotting going on. I color coded the two interlaced systems.
The pinwheel behaves like a tail for the interlaced leading projections. All told this leant a dynamic view of the "herd" behaving as a school.
Presently, though, it can be determined that the markets have only one pattern and this deduced pattern interconnects all fractals in a fixed ratio one to another in the sense of a repeating pattern.
I liked the cubic spline and I'm sure it would have been more fun than the linear MLR's I used.
Because prediction is not necessary and this, once deduced from logic and information theory, all of trading becomes an application of finite maths. you have to use binary vectors to achieve sufficiency and, then certainty as a consequence.
Use a pinwheel for a while and see if the "schooling" of the "herd" becomes quite evident. Front running the herd is how to optimize pool extraction money velocity.
Attached is what I am looking at for tomorrow's trades. Sorry about the sizing.
