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.
I am a degreed Nuclear Engineer with several U.S. patents in radiation shielding design and robotics. I have been trading full-time for 17 years, and I use MatLab and Statistica on cleaned one-minute tic data to develop my trading models. (Seriously, all true) So, due to the technical nature of this discussion I must weigh in with my own cerebral manifesto: The future will not be linear, and that is a certainty. There. Done. That is all.
In a family of interpolation curves that may approximate any future development there is a good chance that one of them would be pretty close to linear. So, the "certainty" about the future could be as uncertain as any other probable walk in this wonderful world of ultimate Randomness. The certainty is that nobody can be certain of anything.
Maestro: I CERTAINLY agree with you. (Hah!, had to do that) The very best I can do for myself and my clients is to find the very best risk/reward skews and try to translate that into as simplistic a mechanical entry system as practicable. The exit is much more complex than the entry. True with trading positions, true with trading systems, true with relationships, true with life. 'Ya know, I should copyright that statement.
I`m enjoying this thread also. But it does aggravate me a bit that it took me years of self education and pain to figure these methods out on my own, with no formal education or mentoring.
We are in the same boat. The further you take your "Technical Analysis" though the more it will lead you here.
I LOVE self education! I think it's THE key to everything! I admire and support people who spend time educating themselves. I am always pleased to help those people if I can and many times I end up learning from them as well. In a mean time, let us come back and discuss this:
Here is some background on the quoted formula. http://mathworld.wolfram.com/RandomWalk1-Dimensional.html.
Ok, I'll make a random observation, it seems interesting that the formula for the expectation value of the absolute distance only depends on the number of steps, not any of the other parameters of the walk. The text at the bottom of the page is also interesting 'Tóth (2000) has proven that there are no more than three most-visited sites in a simple symmetric random walk in one dimension with unit steps'.