A cubic Bézier curve, commonly used in computer graphics to model smooth curves. Adapting it as an indicator for predicting stock price movements involves translating the concept into a financial context.
The Bézier curve equation:
b(t) = (1-t)³ * p0 + 3*(1-t)²t * p1 + 3(1-t)*t² * p2 + t³ * p3
where:
- t is the parameter (usually between 0 and 1).
- P0,P1,P2,P3 are control points, which determine the shape of the curve.
In a stock prediction context:
P0: Initial stock price (or a starting reference point in the past).
P1,P2: Control points to shape the trajectory, which could be derived from technical indicators or recent price trends.
P3: Target or expected stock price, which can be set based on fundamental or technical analysis.
Steps to Apply in Predictive Modeling
Define Control Points (P0,P1,P2,P3):
P0: Use the current or starting stock price.
P1,P2: Derive these points using historical data, moving averages, or significant levels of support/resistance.
For instance, P1 might be based on the recent moving average, and P2 might be a projection based on momentum.
P3: Choose a projected future price based on your prediction model (e.g., based on regression analysis, market sentiment, or fundamentals).
Parameterize t:
t could represent time, normalized between 0 (current moment) and 1 (target time frame for the prediction, e.g., 5 days or 1 week).
Example: If predicting over 5 days, ttt would range from 0 (today) to 1 (Day 5).
Generate the Curve:
Use the Bézier equation to compute B(t) for various values of t. This will produce a smooth curve showing potential stock price movements over time.
Interpret the Curve:
The curve provides a trajectory of potential price movement. Analyze its slope and shape to predict trends:
- Upward curve: Indicates a bullish trend.
- Downward curve: Indicates a bearish trend.
- Flat curve: Indicates consolidation.
Relation between Python and Cubic Bezier:
Calculating and using Cubic Bezier curves in Python is quite straightforward. Libraries used for mathematical calculations like numpy can be employed to create and manipulate Cubic Bezier curves. These libraries can easily perform the necessary mathematical operations required to construct Cubic Bezier curves.
Furthermore, Python’s graphic libraries such as matplotlib, PyQtGraph, Plotly, among others, can be utilized to draw and visualize Cubic Bezier curves. These libraries provide convenient tools and functions for drawing Cubic Bezier curves.
The Pine Code Will Look Something Like This:
//@versio=5
indicator(“Bézier Curve Prediction”, overlay=true)
// Input control points
P0 = input(close, “P0 (Starting Price)”)
P1 = input(close * 1.02, “P1 (Control Point 1)”)
P2 = input(close * 1.04, “P2 (Control Point 2)”)
P3 = input(close * 1.06, “P3 (Target Price)”)
// Input time frame for prediction
num_steps = input(50, “Number of Steps (Resolution)”)
// Bézier Curve Calculation
var float[] bezier_values = array.new_float(num_steps)
for i = 0 to num_steps – 1
t = i / (num_steps – 1)
B_t = (1 – t)^3 * P0 + 3 * (1 – t)^2 * t * P1 + 3 * (1 – t) * t^2 * P2 + t^3 * P3
array.set(bezier_values, i, B_t)
// Plot the Bézier curve
for i = 0 to num_steps – 2
plot(array.get(bezier_values, i), color=color.new(color.blue, 50), linewidth=2)
// Optional: Plot control points
plot(P0, color=color.red, style=plot.style_circles, title=”P0″)
plot(P1, color=color.green, style=plot.style_circles, title=”P1″)
plot(P2, color=color.green, style=plot.style_circles, title=”P2″)
plot(P3, color=color.red, style=plot.style_circles, title=”P3″)