HAC-Adjusted Information Coefficient

An information coefficient (IC) series can be autocorrelated because adjacent forward-return labels overlap. A naive t-test treats the observations as independent and can understate uncertainty. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors account for this dependence.

Compute HAC statistics

import numpy as np

from ml4t.diagnostic.metrics import compute_ic_hac_stats

rng = np.random.default_rng(42)
innovations = rng.normal(loc=0.015, scale=0.08, size=252)
ic_series = np.empty_like(innovations)
ic_series[0] = innovations[0]
for index in range(1, len(ic_series)):
    ic_series[index] = 0.5 * ic_series[index - 1] + innovations[index]

stats = compute_ic_hac_stats(
    ic_series,
    label_horizon=5,
    kernel="bartlett",
    use_correction=True,
)

print(f"Mean IC: {stats['mean_ic']:.4f}")
print(f"HAC standard error: {stats['hac_se']:.4f}")
print(f"HAC t-stat: {stats['t_stat']:.2f}")
print(f"Two-sided p-value: {stats['p_value']:.4f}")
print(f"Naive t-stat: {stats['naive_t_stat']:.2f}")
print(f"Lags used: {stats['effective_lags']}")
print(f"Kernel: {stats['kernel']}")
print(f"Small-sample correction requested: {stats['use_correction']}")

Pass the forward-return horizon through label_horizon. When maxlags is not set, the implementation uses the larger of the automatic Newey-West lag and label_horizon - 1, capped at half the sample size.

Inputs and outputs

compute_ic_hac_stats accepts a NumPy array or a pandas or Polars DataFrame. For a DataFrame, set ic_col to the IC column name.

The returned dictionary contains the mean IC, HAC standard error, t-statistic, two-sided p-value, sample count, lag count, kernel, correction setting, and the corresponding naive standard error and t-statistic. With use_correction=True, statsmodels multiplies the HAC covariance matrix by n / (n - k). Here k = 1 because the mean test fits an intercept only.

Interpretation

• Compare hac_se with naive_se to measure the effect of serial dependence.
• Test significance with p_value, not a fixed t-statistic threshold.
• Report label_horizon, effective_lags, sample count, kernel, and use_correction with results.
• Treat HAC as an inference correction. It does not correct biased labels or data leakage.

See statistical tests for DSR and other multiple-testing corrections.