Video of Dual Polynomial Projection

Dual Polynomial Projection

The Dual Polynomial Projection indicator is designed to help predict future price movements on a chart. It uses a mathematical technique called polynomial regression, which allows it to fit a curved line to past price data and then project that line into the future. Simply, it uses past price data to draw lines that show where the price might go next.

 

What is Polynomial Regression?

It’s a type of statistical method used to model the relationship between a dependent variable (like stock prices) and one or more independent variables (like time). Unlike simple linear regression, which fits a straight line through the data points, polynomial regression fits a curved line. The curve can bend and adjust more freely, making it suitable for capturing more complex patterns that aren't straight.

 

How It’s Calculated:

Thanks to LuxAlgo for his assistance in explaining this to me.

In polynomial regression, the data is fitted using a ‘polynomial’ equation, which looks something like this:

y=a0​+a1​x+a2​x2+…+an​xn

Here, y represents the predicted price, x represents the independent variable (like time), and a0​+a1​x+a2​ are the coefficients that determine the curve’s shape. The term n represents the degree of the polynomial, which controls how flexible the curve is. Higher degrees mean more bends in the curve.

The calculation involves setting up a "design matrix" of the input values (like the past prices), and then solving for the coefficients that minimize the difference between the curve and the actual data points.

 

What Does Overfitting Mean in Polynomial Regression?

Overfitting happens when the regression curve tries too hard to fit every data point perfectly. Imagine drawing a line that twists and turns to touch every single point on a scatter plot—this might look great for specific data but will likely perform poorly when predicting new, unseen data. Overfitting means the model is too complex and picks up noise (random fluctuations) rather than the true underlying trend.

 

Effects of Overfitting:

  • Poor Future Predictions: Because the curve is overly tailored to past data, it doesn’t generalize well to future data. This makes predictions less reliable.
  • Increased Sensitivity to Market Noise: Market noise refers to random price movements that don’t reflect the overall trend. A higher-degree polynomial might interpret these random movements as significant patterns, leading to misleading projections.

One way to manage overfitting is by controlling the degree of the polynomial. Keeping the degree too high can result in overfitting, while a lower degree might not capture enough of the trend.

 

How Does the Indicator Work?

The Dual Polynomial Projection indicator doesn’t just use one polynomial regression—it uses two, each slightly different, to provide a more comprehensive look at potential future price movements. Here’s how it does this:

  • Setting Up Two Projections:
    1. Projection 1 uses a set period length (let’s say 100 past bars) and applies a polynomial curve of a specified degree (e.g., degree 3). This projection shows one possible future trend line based on this set of past data.
    2. Projection 2 adjusts slightly - using a period that’s 5% shorter and a polynomial degree that is one level higher than the first projection. This creates a different, faster reactive curve.
  • Calculating the Curves:
    1. The script sets up arrays and matrices for both projections, storing past price data and then solving for the curve’s coefficients.
    2. The calculated projections are then plotted on the chart, with each line showing a different possible future based on the slight differences in the data it used.

 

  • Visual Differences:
    1. The indicator uses different colors for uptrends and downtrends, making it easy to see whether the projections are showing potential price increases or decreases. It also uses unique colors to distinguish the two forecast lines.

 

Why Use Two Projections Instead of One?

Using two projections helps provide a broader perspective. If both projections show similar trends, it can confirm the strength of the prediction. However, if the two lines diverge significantly, it might indicate uncertainty or a potential change in the trend.

  • Adjusting Period Lengths and Degrees: Start by experimenting with different period lengths and polynomial degrees. Lower degrees (like 2 or 3) will give you smoother, less reactive curves, which can be more reliable in predicting broader trends. Higher degrees can capture short-term shifts but may risk overfitting.
  • Comparing Trends: Look at where the two projection lines intersect or diverge. If one line predicts an uptrend while the other shows a downtrend, it’s a signal to be cautious - market conditions might be less predictable at that moment.
  • Locking Projections: If you find a set of parameters that seem to work well, you can "lock" the projection, preventing it from recalculating with every new bar. I added this feature as it may be helpful for taking a snapshot of the market’s forecast at a specific point in time.

 

Reading the Projections:

  • Trend Confirmation: If both projections consistently show an uptrend, it’s a stronger signal that prices might continue to rise. Similarly, if both show a downtrend, it could indicate further declines.
  • Signal Divergence: Divergence between the two lines could suggest indecision in the market, prompting you to look for additional confirmation from other indicators before making a trading decision.

Dual Polynomial Projection GitHub Link