Binary Split

The Binary_Split command identifies structural breaks, or regime shifts, in the relationship between two time series. The algorithm recursively partitions the sample into periods where a simple regression provides the best fit, allowing users to see how relationships change through time.

Example

binary_split(last(vixcls,360),last(sp500,360))

This example examines the relationship between the CBOE Volatility Index (VIX) and the S&P 500 over the last 360 observations. The routine detects periods where the volatility-equity relationship changed significantly and estimates a separate regression for each regime.

Syntax

binary_split(dependentSeries, explanatorySeries)

The command requires two time series of the same frequency and date range. The first series is treated as the dependent variable, while the second series is used as the explanatory variable.

Output

The command produces two complementary panels.

• Regime Analysis Chart – Displays the actual observations, segmented into statistically distinct periods. Each numbered marker identifies a breakpoint where the relationship changed. Separate regression lines are fit to each regime, and the corresponding R² values are shown in the legend.
• Breakpoints represent dates where splitting the sample produces the greatest reduction in total regression error.

How the Algorithm Works

The routine begins by evaluating every possible split date and selecting the breakpoint that minimizes the combined sum of squared residuals from two separate regressions. The same process is then applied recursively to each sub-period, producing a binary tree of regime changes.

To prevent overfitting, each regime must contain a minimum number of observations (currently 30).

Event Annotation Panel

• Breakpoint Annotations – Lists the dates associated with each numbered split and provides contextual events occurring near those regime changes.
• These annotations help explain why the statistical relationship may have shifted, linking model results to economic, political, or market developments.

Typical Use Cases

• Detecting changes in market behavior before and after major events.
• Studying the impact of economic policy, tariffs, legislation, or central bank actions.
• Identifying shifts in macroeconomic relationships across business cycles.
• Finding structural breaks prior to building forecasting models.

Notes

Binary Split is an exploratory diagnostic tool. Breakpoints indicate statistically meaningful changes in a relationship but do not establish causation. Results should be interpreted alongside economic reasoning, sample size, data quality, and other relevant factors.

The command is especially effective when viewed through the slideshow() function, which allows users to step through each identified regime and its associated annotations.

Run this example in RainbowStats