Quote from CGNobody:
I think assuming a winning trading strategy only equals to 10 simple math transforms is very naive.
Simply dealing with risk management could require 10 transforms in the simplest of systems. Any simple entry will require 10 of its own, then 10 for exits. And then try to guess the formula that will describe a system with 30 degrees of liberty and you'll be old before you even cover the possibilities superficially.
Even a system with only 10 variables is considered a bitch to solve mathematically speaking.
Sorry if you misunderstood my point. Let's say to be very precise, 10 or 20 matematical operators regardless of whre or how oftgen they are used. I'll start the list, please add to it and lets see how many we have:
1) addition
2) subtraction
3) multiplication
4) division
5) comparison >, < =
6) please add your selections......
7)
8))
9)
10)
Below is a very advanced list to give you some ideas. But how many trading system use many or all of these?
Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients.
Polynomials: Can be generated by addition and multiplication alone.
Linear function: First degree polynomial, graph is a straight line.
Quadratic function: Second degree polynomial, graph is a parabola.
Cubic function: Third degree polynomial.
Quartic function: Fourth degree polynomial.
Quintic function: Fifth degree polynomial.
Sextic function: Sixth degree polynomial.
Rational functions: A ratio of two polynomials.
Nth root
Square root: Yields a number whose square is the given one .
Cube root: Yields a number whose cube is the given one .
[edit] Elementary transcendental functions
Transcendental functions are functions that are not algebraic.
Exponential function: raises a fixed number to a variable power.
Hyperbolic functions: formally similar to the trigonometric functions.
Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials.
Natural logarithm
Common logarithm
Binary logarithm
Indefinite logarithm
Power functions: raise a variable number to a fixed power; also known as Allometric functions; note: if the power is a rational number it is not strictly a transcendental function.
Periodic functions
Trigonometric functions: sine, cosine, tangent, etc.; used in geometry and to describe periodic phenomena. See also Gudermannian function.
Sawtooth wave
Square wave
Triangle wave
[edit] Special functions
[edit] Basic special functions
Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset.
Step function: A finite linear combination of indicator functions of half-open intervals.
Floor function: Largest integer less than or equal to a given number.
Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function.
Sign function: Returns only the sign of a number, as +1 or −1.
Absolute value: distance to the origin (zero point)
[edit] Number theoretic functions
Sigma function: Sums of powers of divisors of a given natural number.
Euler's totient function: Number of numbers coprime to (and not bigger than) a given one.
Prime-counting function: Number of primes less than or equal to a given number.
Partition function: Order-independent count of ways to write a given positive integer as a sum of positive integers.
[edit] Antiderivatives of elementary functions
Logarithmic integral function: Integral of the reciprocal of the logarithm, important in the prime number theorem.
Exponential integral
Trigonometric integral: Including Sine Integral and Cosine Integral
Error function: An integral important for normal random variables.
Fresnel integral: related to the error function; used in optics.
Dawson function: occurs in probability.
[edit] Gamma and related functions
Gamma function: A generalization of the factorial function.
Barnes G-function
Beta function: Corresponding binomial coefficient analogue.
Digamma function, Polygamma function
Incomplete beta function
Incomplete gamma function
K-function
Multivariate gamma function: A generalization of the Gamma function useful in multivariate statistics.
Student's t-distribution
[edit] Elliptic and related functions
Elliptic integrals: Arising from the path length of ellipses; important in many applications. Related functions are the quarter period and the nome. Alternate notations include:
Carlson symmetric form
Legendre form
Elliptic functions: The inverses of elliptic integrals; used to model double-periodic phenomena. Particular types are Weierstrass's elliptic functions and Jacobi's elliptic functions.
Theta function
Closely related are the modular forms, which include
J-invariant
Dedekind eta function
[edit] Bessel and related functions
Airy function
Bessel functions: Defined by a differential equation; useful in astronomy, electromagnetism, and mechanics.
BesselâClifford function
Legendre function: From the theory of spherical harmonics.
Scorer's function
Sinc function
Hermite polynomials
Chebyshev polynomials
[edit] Riemann zeta and related functions
Riemann zeta function: A special case of Dirichlet series.
Dirichlet eta function: An allied function.
Hurwitz zeta function
Legendre chi function
Lerch transcendent
Polylogarithm and related functions:
Incomplete polylogarithm
Clausen function
Complete FermiâDirac integral, an alternate form of the polylogarithm.
Incomplete FermiâDirac integral
Kummer's function
Spence's function
Riesz function
[edit] Hypergeometric and related functions
Hypergeometric functions: Versatile family of power series.
Confluent hypergeometric function
Associated Legendre functions
Meijer G-function
[edit] Iterated exponential and related functions
Hyper operators
Iterated logarithm
Pentation
Super-logarithms
Super-roots
Tetration
Lambert W function: Inverse of f(w) = w exp(w).
Ultra exponential function
[edit] Other standard special functions
Lambda function
Lamé function
Mittag-Leffler function
Painleve transcendents
Parabolic cylinder function
Synchrotron function
[edit] Miscellaneous functions
Ackermann function: in the theory of computation, a computable function that is not primitive recursive.
Dirac delta function: everywhere zero except for x = 0; total integral is 1. Not a function but a distribution, but sometimes informally referred to as a function, particularly by physicists and engineers.
Dirichlet function: is an indicator function that matches 1 to rational numbers and 0 to irrationals. It is nowhere continuous.
Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
Minkowski's question mark function: Derivatives vanish on the rationals.
Weierstrass function: is an example of continuous function that is nowhere differentiable