Inherent in your statement is a contradiction that does indeed proffer a hardy guffaw of ingorance. Again, however, with that said, i am not seeking a "holy grail"; merely tools. To state that the markets are random is to forsake the phsycological nature of the markets themselves; why for else would we have trends at all (at every time frame)? I guess my question should be debased to: has anyone developed or worked with indicators derived from calculus or the physical sciences. Algebra is only useful as far as it's application, and much of the application is often applied to formulae derived from "higher maths" Obviously statistics does have it's merit (again) and to say that it is a fools endeavour is (again) to say that any sort of analysis of any availible informaiton what-so-ever is futile. It obviously isn't; the fatuity is a consequence of (mis)interpretation. I should digress and note that i consider probability a fundamental component of statistics ( nq, np, SQRT NPQ, etc..) Certainly someone who frequents the Technical Analysis forum has some wisdom to impart. I have started developing a -simple- indicator based upon kinematics and will provide information and statistics Once it's somewhere near completion.
Everyone is entitled to their opinion and their science. Sorry your arrogance won't allow you to view the potential with an open mind. God save the Queen.
There is some very rich and deep information on your quest to be found in the realm of indicators. The spectrum of indicators is very broad as well. Market pace and market sentiment each deal, respectively, with the market and trader in the three applications of maths of interest to you. If you wish to combine all three in one fell swoop (price only), then use three MLR's and measure the rate of change of the three pairs of angular velocities generated. It is better to use concepts that deal with at least three direct variables of the market. This in hand, you can use all of your preferences mathematically speaking. My personal preference would be to use something kindred to the algebra for base five as a starter.
Of course kinematics can and have been applied to markets. Velocity, acceleration, and momentum are old hat, used daily, and written about by many. If you are just getting into this stuff, take a look at Kaufman's book. And then you can branch out into price series work, cycles, etc. Many have gone before you so don't reinvent the wheel.
He needs a quadruple Ph.D. apparently to realize what probability and statistics are about and how they should be applied.
Seemingly all math majors would or should understand how statistics and probabilities should be applied. What I am stating is, my opinion is that statistics and probabilities have no business being applied to the price action of the Markets. Now understand that my opinion is based solely on how "I" trade not anyone else. I understand that a great number of traders use statistics and probabilities in their trading. This explains why those individuals think trading and gambling belong in the same classification. I personally agree with my math professor, anything that CAN be manipulated AT SOME POINT WILL be manipulated so stay the hell away from that which CAN be manipulated and you never have to be disappointed with inconsistent results.
The ultimate fusion of time series, random variation, and kinematics is Kalman filtering. Spend a month learning the math and try a third order filter. Easy to program with a math package with matrix manipulation. It's a lot easier to understand than SCT. And factually based.
^^^ you can't build something to predict the market, only respond to it my background is in statistics&actuarial science; i remember years ago going 'oh boy! now i'm a math brain i'm going to rape the market!!!' I was in for a big suprise. If you want math+market, go into option theory, not technical trading.
The closest approximation of the differential [in some EOD chart] is the ROC indicator, when you decrease the time interval down to 1 bar. It is quite fuzzy and never seen any use. A much better approach is my RELATIVE SLOPE indicator. See http://www.amibroker.com/library/detail.php?id=43 for the details [also built-in indicator in Wealth-Lab and some other T/A softwares]. The RELATIVE SLOPE signals are, sometimes, quite fast and its negative divergence is always interesting, especially when combined with Stochastic and/or MACD divergence. I have also created T/A approximations to the integral of a variable, useful for some specific futures.