Using the Chi-Squared Test to Detect Market Regimes (Bull vs. Bear)

Understanding market regimes is essential for building robust quantitative trading strategies. Whether you're developing a trend-following system or a mean-reversion model, knowing whether the market is in a bullish or bearish phase can dramatically improve your signal quality.

Blending options theory, statistics, and machine learning for smarter trades.

One statistical tool that can help validate regime-dependent patterns is the Chi-Squared test. This test allows you to determine whether certain patterns—like price behavior relative to moving averages—occur more frequently in one regime than another.

Step 1: Define Market Regimes

Before applying the Chi-Squared test, label your data with categorical regime identifiers. Common methods include:

• Golden Cross: 20-period MA crosses above 50-period MA → Bull
• Death Cross: 20-period MA crosses below 50-period MA → Bear
• Price Position: Price above MA → Bull; Price below MA → Bear

df['regime'] = np.where(df['price'] > df['50MA'], 'Bull', 'Bear')

Step 2: Define the Pattern You Want to Test

Choose a pattern that might behave differently across regimes. For example, price position relative to the 20-period MA:

df['pattern'] = np.where(df['price'] > df['20MA'], 'Above', 'Below')

Step 3: Build a Contingency Table

This table summarizes how often each pattern occurs in each regime:

contingency = pd.crosstab(df['regime'], df['pattern'])

Step 4: Run the Chi-Squared Test

Apply the test to determine if the pattern distribution is independent of the regime:

    from scipy.stats import chi2_contingency
    
    chi2, p, dof, expected = chi2_contingency(contingency)
    
    print(f"Chi-squared: {chi2:.4f}")
    print(f"P-value: {p:.4f}")
      

Interpretation

• Low p-value (< 0.05): The pattern is not independent of the market regime → more likely in bull or bear markets.
• High p-value (> 0.05): The pattern appears randomly across regimes → no strong association.

Use Cases in Quant Strategy

• Are breakout signals more common in bull markets?
• Do mean-reversion setups occur more frequently in bear markets?
• Are volume spikes tied to regime shifts?
• Is RSI overbought/oversold behavior regime-dependent?

By running the Chi-Squared test across multiple patterns, you can build a regime-aware signal library that enhances your strategy’s adaptability and robustness.

Next Steps

Once you've identified regime-sensitive patterns, consider:

• Incorporating regime filters into your trading logic
• Weighting signals differently depending on regime
• Using regime classification as a feature in machine learning models

Want to learn how to define regimes using exploratory data analysis? Check out our EDA guide.