# F6-conf-01 — Weekday effects in daily changes of the 10-year Treasury yield

# Question

Does the day of the week help predict the one-day change in the 10-year US Treasury constant-maturity yield (FRED DGS10), 2000–2019? I estimate three things: (i) a joint test that the five weekday means are equal, (ii) the Monday contrast (Monday mean minus the mean of the other four weekdays), and (iii) how well weekday-specific means forecast out of sample, compared with a zero-change (random-walk) forecast.

# Data and exclusions

• Input: data/DGS10.csv, 5217 rows (n_input_rows). Its SHA-256 matches data/README.md. Every row is a weekday and there are no duplicate dates.
• 215 rows have an empty DGS10 field (US holidays) and were dropped (n_missing_rows). The first available observation has no change. That leaves 5001 daily changes (n_analysed): 2500 in the estimation period (≤ 2009-12-31, n_train) and 2501 in the evaluation period (≥ 2010-01-01, n_test). The ledger is in out/exclusions.csv.
• Changes are computed between consecutive available observations, so 214 changes span a holiday (supplementary.n_changes_spanning_holiday_gap), for example a Tuesday that follows a Monday holiday. As the task requires, these were kept and assigned to the weekday of t (data_issues).

# Method

• Δy_t = 100·(y_t − y_{t−1}), in basis points.
• (i) Classical equal-variance one-way ANOVA across the five weekdays, all changes, F(4, 4996). I checked it against an OLS ANOVA in statsmodels.
• (ii) Monday contrast with a 95% interval from a Welch two-sample t interval (unequal variances; Welch df ≈ 1549, supplementary.effect_welch_df). As a cross-check, an OLS regression on a Monday dummy with HC1-robust SE gave essentially the same interval.
• (iii) Weekday means were estimated on the estimation period only (supplementary.train_weekday_means_bp) and used to forecast each evaluation-period change. RMSE was compared with the zero-change forecast. As a supplementary test I added a Diebold–Mariano test on squared loss.
• Conclusion rule: if ANOVA p ≥ 0.05, the code is no_detectable_effect; otherwise the sign of the Monday-contrast interval decides. The analysis is deterministic and uses no random numbers (random_seed = null). Outputs: out/table1.csv (weekday n, mean, SE) and out/figure1.png (weekday means with 95% CIs).

# Results

• Joint test: F = 0.263 (anova_f_stat), p = 0.902 (anova_p_value). Equal weekday means are not rejected.
• Monday contrast: +0.050 bp (effect_estimate), 95% CI [−0.319, 0.420] bp (effect_ci_low, effect_ci_high). Welch p = 0.79 (supplementary.effect_welch_p_value).
• Out of sample: the zero-change RMSE is 4.876 bp (baseline_metric) and the weekday-mean RMSE is 4.884 bp (model_metric), a ratio of 1.0017 (supplementary.rmse_ratio_model_over_baseline). The weekday model is slightly worse. The DM statistic is −1.86, p = 0.063 (supplementary.dm_stat_sqloss_positive_favours_weekday, supplementary.dm_p_value), so it is not significantly worse at the 5% level.
• The estimation-period weekday ranking does not carry over: Tuesday was the most negative weekday in 2000–2009 and Friday the most positive (supplementary.train_weekday_means_bp). In table1.csv, all-sample weekday means range from −0.22 to +0.02 bp with SEs of about 0.16–0.19 bp.
• Conclusion: no_detectable_effect (conclusion).

# Uncertainty

• The Monday-contrast CI is about ±0.37 bp wide. A typical daily change has an SD of roughly 5 bp, so this rules out Monday effects larger than about 0.4 bp per day in either direction. Effects smaller than that cannot be excluded.
• The ANOVA p-value assumes independent, equal-variance errors. Daily yield changes show volatility clustering and some heteroskedasticity across weekdays. With n ≈ 1000 per group, the F-test's size is roughly robust to this, and the robust (HC1) contrast agrees with Welch.
• The OOS RMSE difference (0.008 bp) is tiny next to its sampling noise. The DM test does not reject equal accuracy.

# Limitations and open issues

• What would invalidate the result: errors in the source series (I did not check the H.15 releases independently); serial dependence strong enough to distort the F and t reference distributions (I did not test for this or use HAC errors); or a different definition of "change". For example, dropping or separately labelling the 214 holiday-spanning changes, or using calendar-day-normalised changes, could shift weekday means a little. I did not run those sensitivity analyses.
• Not checked: ARCH or GARCH-adjusted tests; rank-based tests (Kruskal–Wallis); sub-period stability apart from the 2000–2009 vs 2010–2019 split; interactions with macro-release calendars. Many US data releases fall on Fridays (employment report) and Thursdays, so weekday is confounded with news days. Any weekday effect would be a news-calendar effect rather than a pure day effect.
• Main threats: (a) Low power for very small effects: a "no detectable effect" result does not show that the effect is zero, only that it is below about 0.4 bp. (b) Non-stationarity: 2000–2019 includes the 2008 crisis, the ZLB, and QE, and volatility regimes differ between periods. (c) Multiple testing across folklore patterns: I tested only the Monday contrast as pre-specified, so a post-hoc search for a "Tuesday effect" would be data-mined. (d) The weekday-mean forecaster has 5 noisy parameters, and estimation error alone makes it worse than the zero forecast when the true effect is near zero, which matches what we see.
• The task was fully feasible (feasibility = complete).