Stationarity Tests

Feeding non-stationary features (raw prices, trending volume) into ML models produces spurious correlations that vanish out of sample. Test stationarity first, transform if needed.

The Problem

Raw asset prices are non-stationary: their mean and variance change over time. A regression of one non-stationary series on another can produce high R-squared and significant t-statistics even when there is no causal relationship (spurious regression). In ML4T, this means a model trained on raw prices will appear to predict well in-sample but fail live. Returns and most financial ratios are stationary. The gap between "looks predictive" and "is predictive" often comes down to stationarity.

The Pattern

WRONG

import numpy as np
from sklearn.linear_model import Ridge

# Model raw prices - non-stationary, spurious correlation
X = price_features  # Trending upward
y = forward_prices  # Also trending upward
model = Ridge().fit(X, y)
print(f"R-squared: {model.score(X, y):.3f}")  # High but meaningless

CORRECT

import numpy as np
from statsmodels.tsa.stattools import adfuller, kpss

def test_stationarity(series):
    """Run ADF and KPSS tests. Both must agree."""
    series = series[~np.isnan(series)]
    adf_stat, adf_pval, *_ = adfuller(series, autolag='AIC')
    kpss_stat, kpss_pval, *_ = kpss(series, regression='c', nlags='auto')
    return {
        'adf_pval': adf_pval,     # H0: unit root (non-stationary)
        'kpss_pval': kpss_pval,   # H0: stationary
        'stationary': adf_pval < 0.05 and kpss_pval > 0.05
    }

# Test before modeling
for col in ['price', 'returns', 'momentum_12m', 'volatility_20d']:
    result = test_stationarity(features[col].to_numpy())
    status = "OK" if result['stationary'] else "TRANSFORM"
    print(f"{col:>20}: ADF p={result['adf_pval']:.3f}, "
          f"KPSS p={result['kpss_pval']:.3f} -> {status}")

Decision Matrix

ADF rejects H0?	KPSS rejects H0?	Conclusion	Action
Yes	No	Stationary	Use as-is
No	Yes	Non-stationary	Difference or use returns
Yes	Yes	Trend-stationary	Remove trend, then use
No	No	Inconclusive	Get more data or use returns

Making Features Stationary

# Method 1: First difference (simplest)
diff = series.diff().dropna()

# Method 2: Log returns (standard for prices)
log_ret = np.log(series / series.shift(1)).dropna()

# Method 3: Fractional differentiation (preserves memory)
# d=1.0 is full differencing; d=0.3-0.5 balances stationarity + memory
from fracdiff import fdiff
frac_diff = fdiff(series.to_numpy(), d=0.4)

Guardrails

• Always run BOTH ADF and KPSS - they have opposite null hypotheses and catch different failures
• KPSS is sensitive to lag selection; use nlags='auto' to avoid misleading results
• Returns are almost always stationary; prices almost never are
• Non-stationary features can still be useful inside tree-based models (which split on rank), but regularized linear models and neural networks require stationarity
• After transformation, verify IC is preserved - aggressive differencing can destroy signal

Production Implementation

ml4t-diagnostic provides batch stationarity testing:

from ml4t.diagnostic.evaluation.stationarity import analyze_stationarity

result = analyze_stationarity(feature_series, include_tests=["adf", "kpss"])
print(result.consensus)
print(result.summary_df)

Checklist

• Both ADF and KPSS tests run on every feature
• Non-stationary features transformed (differencing, returns, or frac-diff)
• Transformation method documented per feature
• IC compared before vs after transformation to verify signal preservation
• Tree models distinguished from linear/DL models in stationarity requirements