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A disparate, hardly up to date algorithmic trading framework/system. Or better put, a collection of various scripts to put one together yourself... sort of.

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xaviergoby/AI-Algorithmic-Trading-System

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Forecasting with Fast Fourrier Transformations (FFT's)

Problem: How do I decompose a time-series into something simple (for then performing forecasting with it)?

Key Idea: Decomposition

Main idea (Key to the Algo): A reasonably continouos and periodic function can be represented/expressed as the sum of a series of sine functions/keys.

Sine/Sinusoidal Function: f(t) = Asin(wt + theta)

Where:

  • A: Amplitude
  • w: angular frequency
  • theta: Phase-shift

Period: T = 2pi / w

If I can apply a forecasting technique to each of my sine functions/signals obtained from my OG time-series then I can then recombine my forecastings and get my forecasting result.

The more and more sine functions I use/apple, the better my approximation of the OG TS becomes.

FFT Steps:

  1. Fun FFT on input data
  2. Filter out low-amplitude or high-frequency components. Data which has very low-amp and/or high-freq is most likely noise b/c it happens very frequently and very irregularly.
  3. Pick the first few most significant sine functions
  4. Apply forecast on each of the individual components (sine functions/signals). Basically I need to move my phase forward (heh?).
  5. Recombine the result of the above in order to get my final forecast.

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