Quantitative Statistical Methods

Overview

Common statistical methodology used in quantitative investing, covering time-series testing, volatility modeling, regression diagnostics, and statistical inference. Provides the statistical foundation for strategy development and factor research.

Implementation

Every test below is already implemented and unit-tested in src.quantlib.timeseries. Import and call it, do not retype these formulas into throwaway code, which is how sign errors and double-sqrt bugs get into results.

from src.quantlib.timeseries import (
    adf_test, cointegration_test, find_hedge_ratio, compute_half_life,
    granger_test, fit_garch, heteroscedasticity_test, autocorrelation_test,
    vif_test, bootstrap_statistic, bootstrap_sharpe,
)

Optional backends: statsmodels powers everything except the two bootstrap helpers (which are pure numpy); arch powers fit_garch only. Neither is declared as a dependency of vibe-trading-ai, so both are imported lazily inside the functions. Importing the module always works; calling a function whose backend is missing raises an ImportError naming the package and the install command (pip install "statsmodels>=0.14" / pip install "arch>=6.0"). If you hit that error, report it to the user rather than silently substituting a different method.

Time-Series Tests

1. ADF Unit-Root Test (Stationarity Test)

Why it matters: regressing non-stationary series directly can produce spurious regression, making conclusions unreliable.

from src.quantlib.timeseries import adf_test

result = adf_test(prices['close'], significance=0.05)
# {'adf_statistic': -1.23, 'p_value': 0.65, 'lags_used': 4,
#  'is_stationary': False,
#  'critical_values': {'1%': -3.44, '5%': -2.87, '10%': -2.57}}

if not result['is_stationary']:
    returns = np.log(prices['close']).diff().dropna()
    adf_test(returns)  # log returns are normally stationary

Decision rules: