fix(ops): unify ddof=0 for ts_covariance, fix corr identity#2
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ts_covariance changed from ddof=1 (sample) to ddof=0 (population) to match the library-wide convention. This fixes the broken identity: ts_covariance(x,y,w) / (ts_std_dev(x,w) * ts_std_dev(y,w)) == ts_corr(x,y,w) Previously the mixed ddof (cov=1, std=0) caused the left side to exceed the true correlation by a factor of n/(n-1). ts_corr and ts_autocorr retain ddof=1 in Polars rolling_corr because Polars applies ddof only to the numerator (cov), producing incorrect results with ddof=0. Correlation output is ddof-invariant so the values are unaffected. Cross-validated against numpy to machine precision (diff < 1e-15). [NUMERICAL] ts_covariance output changes: values are now multiplied by (n-1)/n relative to previous output. For window=20, this is a 5% reduction. ts_corr and ts_autocorr output is unchanged.
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Summary
Unify ddof=0 (population) for ts_covariance. Fixes the broken identity:
ts_covariance(x,y,w) / (ts_std_dev(x,w) * ts_std_dev(y,w)) == ts_corr(x,y,w).
Previously the mixed ddof (cov=1, std=0) caused ~5-20% error depending on window size.
Change Type
Numerical Impact
ts_covariance output changes by factor of (n-1)/n:
ts_corr and ts_autocorr output: unchanged.
Cross-validated against numpy to machine precision (diff < 1e-15).
Testing
pytest tests/ -v)ruff check elvers/)