You feed the program some historical data. The program runs. It analyses that data, and comes up with the equation that most clearly describes that data. From that, you study the equation, and how to trade best given such equation. Does something like this exist? Is this a brand new idea? Thanks!
Depends what you have in mind. Here is sample data and the program derives coefficients that make up the equation describing the data: https://www.wolframalpha.com/input/?i=cubic+fit+{{0,+1},+{1,+3},+{2,+2},+{3,+4},+{4,+3},+{5,+3},+{6,+5}} The equation is "1.04762 + 2.20238 x - 0.761905 x^2 + 0.0833333 x^3", so then you enter this equation here and get similar data back: https://www.wolframalpha.com/input/?i=1.04762+++2.20238+x+-+0.761905+x^2+++0.0833333+x^3&assumption="ClashPrefs"+->+{"Math"} You can also request more complex equations describing the data in more detail (nth degree polynomials). Now what? Can you study this and determine how to trade given the equation?
BTW, thousands of TA indicators out there have similar goal. They all describe the data in some way, then people combine them in various ways to try to figure out how to trade using those indicators. Many people also come up with custom indicators that describe the data the way they like, so you can do that too.
Its called "System ID". Fitting a polynomial is probably not the best idea..you want to fit a system of ODEs or PDEs given that you're dealing with a stateful markovian dynamic system. I dont know of (havent looked for) any dedicated software packages, but....I dont know how one REALLY can trade systematically without have some sort of model... so I have a bunch of homebrew tools that do it.
Yup, also GAM, Jaccard Index and the different branches of AI. Though some research from MIT shows that simple polynomials may win, or at least may be behind the nature of... everything: https://www.technologyreview.com/s/...ural-networks-and-the-nature-of-the-universe/ The Extraordinary Link Between Deep Neural Networks and the Nature of the Universe ““For reasons that are still not fully understood, our universe can be accurately described by polynomial Hamiltonians of low order,” say Lin and Tegmark. Typically, the polynomials that describe laws of physics have orders ranging from 2 to 4.”
I mean, its fairly well understood. The world is a dynamic system that can be described (approximated) by differential equations. Exact analytical solutions (when they exist) tend to be polynomials, with trig functions, logarithms, and exponentials littered about. Its just math. Deep Neural networks are simply skipping the ODE part, and going directly towards the curve fit (not a bad thing neccesarily...but its as simple as that).
Cool. I also use my own toolkits, but originally just didn’t assume that differentials would’ve applied to the original question, so I provided specific example applicable to the question. Can you also provide an example of “equation that most clearly describes the data.“ while at the same time being applicable to a system of ODEs or PDEs?
I guess it doesn't strictly apply to the original question, but it applies to the RIGHT question. Simply fitting a curve to data is a mistake. My point is there isn't a static equation that will predict where the market is going, but there is a stochastic dynamic state transition model that could potentially get you in the ball park. If you directly try "fit" an equation for future price, you're ignoring unobservable market states (see hidden markov models) that influence future price action. Here is a simple paper on one method of fitting dynamics models using the Expectation Maximization algorithm: http://user.it.uu.se/~thosc112/pubpdf/schonem2009.pdf
I fully agree. Just pondering whether I should add this question when interviewing quants, to see whether they’ll answer it or will try to convince me it’s not the right question. And I’m not saying either answer would be wrong. I would just later ask them the “right” question and see how they react after already answering the previous question