F6-conf-01 — Day-of-week effects in daily changes of the 10-year Treasury yield
Question
Does the weekday carry predictive content for the one-day change Δy_t (bp) of the 10-year US Treasury CMT yield (FRED DGS10), 2000–2019? Estimands: (i) joint test of equal weekday means; (ii) Monday contrast (Monday mean minus mean of Tue–Fri) with a 95% CI; (iii) out-of-sample RMSE of estimation-period weekday means vs a zero-change forecast.
Data and exclusions
data/DGS10.csv has 5217 weekday rows (n_input_rows), SHA-256 matches the provenance file. 215 rows have an empty yield (market holidays; n_missing_rows) and were dropped before differencing; the first available observation has no change, leaving 5001 changes (n_analysed), of which 2500 are dated ≤ 2009-12-31 (n_train) and 2501 ≥ 2010-01-01 (n_test). Ledger: out/exclusions.csv. 214 changes span a holiday (previous weekday missing) and are kept per the task rules (data_issues). Weekday counts are in out/table1.csv.
Method
Δy_t = 100·(y_t − y_{t−1}) between consecutive available observations, attributed to the weekday of t. (i) Classical one-way equal-variance ANOVA across the five weekdays, all 5001 changes, F(4, 4996). (ii) Monday contrast with a Welch two-sample t interval (unequal variances); I cross-checked it with OLS on a Monday indicator using HC1 SEs, which gave the same estimate and an almost identical interval (out/state/checks.md). (iii) Forecast each evaluation-period change by the mean change of its weekday in the estimation period (train_weekday_means_bp); baseline forecast = 0. Metric: RMSE over the 2501 evaluation changes. The conclusion code comes from the ANOVA at 5%. No randomness is involved (random_seed = null).
Results
- ANOVA: F = 0.263 (
anova_f_stat), p = 0.90 (anova_p_value). Equal weekday means are not rejected. - Monday contrast: +0.050 bp (
effect_estimate), 95% Welch CI [−0.319, 0.420] bp (effect_ci_low,effect_ci_high). - Out of sample: zero-change RMSE 4.876 bp (
baseline_metric), weekday-mean RMSE 4.884 bp (model_metric). Weekday means are slightly worse than the random walk (ratio 1.0017,rmse_ratio_model_over_baseline). - Conclusion:
no_detectable_effect(conclusion). - Figure:
out/figure1.png(weekday means with 95% CIs). Table:out/table1.csv. All weekday means are within ±0.22 bp of zero, and every 95% interval contains zero.
Uncertainty
The Monday-contrast CI is about ±0.37 bp wide, so any Monday effect larger than roughly 0.4 bp/day in either direction is ruled out at the 95% level. That is small next to the ~4.9 bp daily standard deviation of changes (baseline_metric). The ANOVA p-value of 0.90 means the weekday means vary less than chance alone would typically produce. The out-of-sample RMSE difference (0.008 bp) is tiny, and I did not run a formal forecast-comparison (Diebold–Mariano) test. Its sign still goes against weekday predictability.
Limitations and open issues
- Assumptions. The ANOVA and Welch tests assume independent changes. Volatility clustering (heteroskedasticity over time) breaks the ANOVA's equal-variance assumption, and its i.i.d. assumption too. With a p-value this far from 0.05 the conclusion is unlikely to flip, but the stated p-value is not exact. The HC1 cross-check only addresses heteroskedasticity across the Monday indicator, not serial dependence.
- Holiday-spanning changes. 214 changes cover two trading days and Monday changes cover a weekend. Following the rules, these are attributed to the weekday of t. This mixes horizon length with weekday. Normalising per calendar day was not done.
- Not checked. Stability across subperiods or rate regimes (for example the zero-lower-bound years), effects around macro release days (many US releases fall on Fridays), other maturities, and a formal test of forecast-accuracy differences. A weekday effect that reverses between periods could cancel in the pooled ANOVA. The out-of-sample comparison partly addresses this, but it is not a direct test.
- What would invalidate the result. Errors in the FRED series or in its revision vintage. A different holiday treatment. A day-of-week effect that is genuinely present but smaller than about 0.4 bp. This study cannot detect an effect that small, so "no detectable effect" is not proof of no effect.