I start with a "perfect as it can get" normalized Velocity code, then acceleration and on to jerk. This velocity calculation is a remarkable momentum oscillator that revolutionizes how the rate of price change is measured, offering a significant edge over standard velocity calculations like simple price differences or basic momentum metrics. Unlike typical methods that compute price changes with raw subtractions, resulting in noisy, erratic signals that react to every market fluctuation, this calculation employs a weighted approach that prioritizes recent price movements. By giving more importance to the latest data, it captures the market’s current momentum with exceptional clarity, making it ideal for tick-based charts where price movement patterns, not time intervals, drive trading decisions. This weighted method filters out irrelevant noise, producing a smooth, trend-aligned signal that reflects the market’s immediate dynamics, unlike the choppy outputs of standard calculations. Its brilliance lies in its lag-elimination and adaptive smoothing techniques, which ensure signals are both timely and context-sensitive. Traditional velocity calculations often lag due to long averaging periods or fail to adapt to changing market conditions, leading to delayed or false signals. This calculation counters these issues with exponential decay, emphasizing the most recent price data to keep the signal responsive, and volatility adjustments that scale sensitivity based on market conditions—amplifying signals during sharp moves and dampening them in choppy periods. It is normalized by adjusting the output relative to market volatility, ensuring signals are meaningful across different price environments, whether trending or ranging. The spatial design further distinguishes it, capturing how prices move relative to key levels or trends, not just temporally, making it a spatial velocity tool. This extends to spatial acceleration (rate of change of velocity) and spatial jerk (rate of change of acceleration, derived from acceleration, which comes from velocity, which comes from price), which detect abrupt momentum shifts within the market’s structural context. Unlike standard velocity calculations that overlook these spatial dynamics, this calculation delivers precise, lag-free buy and sell signals, perfectly suited for tick-based charts, providing a powerful, adaptive tool to navigate dynamic markets. Here is the progression on a 40 tick 10 point range bar (timeless data) >spatial. subgraph 1 velocity subgraph 2 acceleration subgraph 3 jerk
I appreciate you first of all. When I started out I was simple as can be in my analysis. I was offered a mentorship with a trader because I was pretty good trading SP's with simple stuff. In a high pressure trading environment pushed to find the grail, with pretty much unlimited resources--I went off the deep end to make it short. I found that keep it simple was (at least for me) a cop out for not doing the required work. Simple to one may mean something different to another. I am thankful and glad I have experienced what I have and been blessed to basically run wild without limitations other than my own. That's when I finally got out of the way and started letting statistics rule the course. Chasing results not notions and accepting facts over fiction. It is what it is when you find it, no matter what you personally think of it. What matters is results no matter the means. EDIT LETS MAKE IT SIMPLE A TRAIN ONCE IN MOTION IS MOST LIKELY TO CONTINUE ON IT'S GIVEN PATH THAN IT IS TO STOP AND REVERSE - RIGHT? OK THE FASTER THE TRAIN IS GOING TO MORE LIKELY THE ABOVE STATEMENT IS TRUE - THAT IS THE HOLY GRAIL. THAT IS PREDICATIVE VELOCITY IS NOT ENOUGH IT TAKES ACCELERATION AND PERFECTION IS NEAR SPITAL (NON TIME BASED) JERK.
I should have dropped this in here the other day for future discussion but I got side tracked. This is an overview of mathematical techniques used in computational modeling and optimization. Here's a breakdown: Fast Marching Method (FMM): This method efficiently propagates information across a grid, often used for shortest path computations in continuous domains. It solves the Eikonal equation, where arrival time T(x)T(x) depends on a speed function F(x)F(x). It uses priority queues for efficient computation, similar to Dijkstra’s algorithm. Level Set Methods: These are used to track evolving shapes and interfaces, such as flame fronts or shape evolution. Instead of explicitly defining a boundary, it represents surfaces as the zero-level set of a higher-dimensional function. It relies on solving Hamilton–Jacobi equations and numerical techniques like ENO/WENO schemes for stability. Variational Methods / Gradient Descent in Shape Optimization: This framework is used for optimizing shapes and paths by minimizing a cost functional. It leverages the calculus of variations to derive Euler–Lagrange equations and often works in infinite-dimensional spaces. Dynamic Programming / Bellman Equations: Used for optimal control and shortest path problems in discrete settings. It is based on the Bellman equation, which recursively finds optimal solutions by minimizing cost functions. In continuous cases, this leads to Hamilton–Jacobi–Bellman PDEs. 1. Fast Marching Method (FMM) Used for: Efficient front propagation on grids (e.g., shortest paths in continuous domains). Mathematical foundation: Solves the Eikonal equation: ∣∇T(x)∣=1F(x)|\nabla T(x)| = \frac{1}{F(x)}∣∇T(x)∣=F(x)1 where T(x)T(x)T(x) is the arrival time of the front at location xxx, and F(x)F(x)F(x) is the speed function. Requires upwind finite difference schemes to ensure stability and correctness. Complexity: Uses a min-heap or priority queue (like Dijkstra’s) for ordering updates efficiently. O(NlogN)O(N \log N)O(NlogN) time where NNN is the number of grid points. 2. Level Set Methods Used for: Modeling moving interfaces (e.g., flame fronts, shape evolution). Core math: Represents surfaces as zero-level sets of higher-dimensional functions. Solves Hamilton–Jacobi equations: ∂ϕ∂t+F∣∇ϕ∣=0\frac{\partial \phi}{\partial t} + F |\nabla \phi| = 0∂t∂ϕ+F∣∇ϕ∣=0 where ϕ(x,t)\phi(x, t)ϕ(x,t) is a signed distance function. Numerical methods: High-order ENO/WENO schemes, reinitialization techniques, and curvature-dependent flow. 3. Variational Methods / Gradient Descent in Shape Optimization Used for: Finding shapes or paths that minimize a cost functional. Math tools: Calculus of variations: Derive Euler–Lagrange equations for minimal paths. Functional minimization over infinite-dimensional spaces. Might involve Riemannian manifolds for geodesics, or Sobolev space embeddings. 4. Dynamic Programming / Bellman Equations Used for: Discrete optimal control, shortest paths. Mathematics: Bellman equation: V(x)=minu{L(x,u)+V(f(x,u))}V(x) = \min_{u} \left\{ L(x, u) + V(f(x, u)) \right\}V(x)=umin{L(x,u)+V(f(x,u))} The continuous analog leads to Hamilton–Jacobi–Bellman (HJB) PDEs, solved numerically or via policy iteration.
Just some good reference material. Trend-Following Filters – Part 8 - It is a series of articles. Just change the last number in the url from 1 to 8.
Hey, what about the Jerk's younger brothers - Snap, Crackle and Pop ??? Would that help ? Hey, by the late 90s they were already evolving price ODEs.
im sure that snap krackle pop can be used for something, but even the jerk is awful fast for automated entry. even the market isn't fast enough all the time to apply those. but sometimes it is and when it is the public data feeds can't keep up. it would be ideal if all data was the same for everyone members and non-members. the term ode like many other terms are always being rediscovered and renamed. the key is to get a handle on velocity first, get it smooth but with no lag - rare event it's a four process event. General Mathematical Principles by markbrown Adaptive Filtering: Adjusting the indicator’s responsiveness based on market conditions (e.g., volatility, trend strength). Digital Signal Processing (DSP): Using techniques like convolution or frequency domain analysis to smooth data. Nonlinear Transformations: Applying proprietary weighting or phase adjustments to reduce lag and noise. Volatility-Based Weighting: Modulating smoothing based on price volatility. This is the process to the best thing I have ever come up with.
To understand how to progress from velocity to "snap, crackle, and pop" in physics, it's helpful to recognize that these terms refer to higher-order derivatives of position with respect to time.Wikipedia+2Wikipedia+2Physics LibreTexts+2 Derivatives of Position Velocity: The first derivative of position, indicating the rate of change of position over time. Acceleration: The second derivative of position, representing the rate of change of velocity. Jerk: The third derivative of position, describing the rate of change of acceleration. Snap (or Jounce): The fourth derivative of position, indicating the rate of change of jerk. Crackle: The fifth derivative of position, representing the rate of change of snap. Pop: The sixth derivative of position, describing the rate of change of crackle.Reddit+4Physics LibreTexts+4Henning's blog+4 These higher-order derivatives are less commonly used but can be important in fields like robotics and aerospace engineering, where smooth trajectories are crucial. Wikipedia Practical Application In trajectory planning, especially for Micro-Aerial Vehicles (MAVs), it's often desirable to minimize jerk to ensure smooth motion. This is known as a "minimum snap trajectory." To achieve this, one might optimize the trajectory by setting the derivative of snap (crackle) to zero, effectively minimizing higher-order derivatives for smoother motion. HandWiki+3Chegg+3Wikipedia+3
given enough datapoints you can predict the future events of any system. but you have to have a processing power greater than that of the system to predict further into the future. we can already predict limited future. we do it on small scale and large scale also. if you are late for work you will get yelled at by your boss.. future predicted. if you dont show up to work you wont get paid if you put your hand in fire you will get burned our brains predict future constantly you just not aware of it. especially when you are driving your brain is constantly running a simulation of immediate events and surroundings to make sure you dont crash ai can gather and organize events and data points on a massive scale that was never possible before. thats why so many institutions are investing in ai. they are using social media and free trading platforms to train the ai to predict future events long term and also to be able to have full control of price movement at every timeframe. ai can respond to price movement in real time based on social media based on the data from order flow. thats why im saying that retail is abotu to get fucked like it never got fucked before. get ready they will have their designated influencers of course to promote trading to attract more people. because ai will be able to recognize trading patterns from specific traders and influence their outcome directly without any paper trail. for example a well known influencer is bringing alot of fresh meat to the market.legally you cant give him signals when to buy and when to sell. but ai can manipulate the chart to show exact chart movement for him to see and make his move and "make millions day trading for 30 minutes a day" a small price to pay to attract noobs with money