POLY_SCATTER Command | RainbowStats

The POLY_SCATTER command creates a scatter plot between two time series and fits a polynomial curve through the relationship. It is designed for exploring nonlinear relationships between economic, financial, and market data series.

Unlike a simple linear scatter plot, POLY_SCATTER allows the fitted relationship to bend. This makes it useful when the relationship between two variables changes as the level of one variable rises or falls.

Example

POLY_SCATTER(LIST(SP500,NQAI),2)

This example compares the S&P 500 with the Nasdaq Global Artificial Intelligence and Big Data Index using a second-degree polynomial fit.

The chart plots the observed data points, the fitted polynomial curve, and standard-deviation bands around the fitted relationship.

Syntax

POLY_SCATTER(seriesList, degree)

The first argument is a list containing two time series. The second argument controls the degree of the polynomial fit.

seriesList — a list containing exactly two aligned time series.
degree — the polynomial degree used for the fitted curve.

A degree of 1 gives a straight-line fit. A degree of 2 gives a quadratic fit. Higher degrees allow more curvature, but may also overfit the data.

Output

The command produces a D3 scatter chart with:

Actual observed data points
The fitted polynomial curve
Positive and negative standard-deviation bands
Axis labels based on the input series names
A chart title identifying the two series and polynomial degree

The standard-deviation bands help show whether recent observations are close to the historical fitted relationship or unusually high or low relative to that relationship.

Interpretation

A polynomial scatter plot is useful when the relationship between two series is not perfectly linear. For example, the stock market may rise with an AI-related index, but the relationship may flatten or steepen at different levels of the index.

The fitted curve should be read as a historical relationship, not as a forecast. Points near the fitted curve are consistent with the past relationship between the two series. Points far above or below the curve may indicate a temporary divergence, valuation gap, regime change, or unusual market condition.

The +1σ, -1σ, +2σ, and -2σ bands provide a visual measure of how far the actual observations are from the fitted polynomial relationship.

Typical Use Cases

Comparing equity indexes with sector or theme indexes
Testing whether two market series have a nonlinear relationship
Finding stretched or compressed relationships between assets
Visualizing valuation gaps
Studying macroeconomic relationships that bend at high or low levels

Additional Examples

POLY_SCATTER(LIST(SP500,NASDAQ100),2)

Compares the S&P 500 with the Nasdaq 100 using a quadratic fit.

POLY_SCATTER(LIST(WTI,OILSTOCKS),2)

Explores a nonlinear relationship between crude oil prices and oil-related equities.

POLY_SCATTER(LIST(DGS10,T10YIE),2)

Compares the 10-year Treasury yield with the 10-year breakeven inflation rate.

Note: Polynomial fits can be visually powerful, but they should be interpreted carefully. A higher polynomial degree can improve the visual fit while reducing the economic meaning of the curve. For most market and macroeconomic applications, degree 1 or 2 is usually the best starting point.

Related Commands

REGRESSION — estimate a linear relationship between time series
ROLL_BETA — estimate rolling market sensitivity
CONSTRAINED_OLS — estimate regression models with coefficient constraints
PC_ANALYSIS — analyze common factors across multiple series