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Stochastic oscillator is a momentum indicator within technical analysis that uses support and resistance levels as an oscillator. George Lane developed this indicator in the late 1950s. [ 1 ] The term stochastic refers to the point of a current price in relation to its price range over a period of time. [ 2 ]
George Lane (1921 – July 7, 2004) was a securities trader, author, educator, speaker and technical analyst.He was part of a group of futures traders in Chicago who developed the stochastic oscillator (also known as "Lane's stochastics"), which is one of the core indicators used today among technical analysts.
An oscillator in technical analysis of financial markets is an indicator that informs if the price of a financial instrument is very high or very low, indicating whether it is overbought or oversold. This helps traders make decisions about when to trade (buy or sell) that instrument.
Here ¯ is the mean number of excitations in the reservoir damping the oscillator and γ is the decay rate. To model the quantum harmonic oscillator Hamiltonian with frequency ω c {\displaystyle \omega _{c}} of the photons, we can add a further unitary evolution:
The relationship between different moving average trading rules is explained in the paper "Anatomy of Market Timing with Moving Averages". [4] Specifically, in this paper the author demonstrates that every trading rule can be presented as a weighted average of the momentum rules computed using different averaging periods.
The Van der Pol oscillator was originally proposed by the Dutch electrical engineer and physicist Balthasar van der Pol while he was working at Philips. [2] Van der Pol found stable oscillations, [3] which he subsequently called relaxation-oscillations [4] and are now known as a type of limit cycle, in electrical circuits employing vacuum tubes.
Phase portrait of damped oscillator, with increasing damping strength. The equation of motion is x ¨ + 2 γ x ˙ + ω 2 x = 0. {\displaystyle {\ddot {x}}+2\gamma {\dot {x}}+\omega ^{2}x=0.} In mathematics , a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane .
The oscillator is on a negative scale, from −100 (lowest) up to 0 (highest), obverse of the more common 0 to 100 scale found in many technical analysis oscillators. A value of −100 means the close today was the lowest low of the past N days, and 0 means today's close was the highest high of the past N days. (Although sometimes the %R is ...