# 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 Δy_t (basis points) in the 10-year US Treasury constant-maturity yield (FRED DGS10) over 2000–2019? There are three estimands: (i) a joint test that the five weekday means are equal; (ii) the Monday contrast (mean on Mondays minus mean on Tuesday–Friday), with a 95% interval; (iii) the out-of-sample RMSE of weekday-mean forecasts against a zero-change forecast.

# Data and exclusions

• Input: data/DGS10.csv, 5217 rows (n_input_rows), one per weekday from 2000-01-03 to 2019-12-31. Its SHA-256 matches data/README.md.
• 215 rows have an empty yield field because of US market holidays, including the 2001-09-11/12 closure (n_missing_rows). These rows were dropped first. One more observation was lost because the first available observation has no change. This leaves 5001 daily changes (n_analysed), see out/exclusions.csv.
• The estimation period (changes dated ≤ 2009-12-31) has 2500 changes (n_train). The evaluation period (changes dated ≥ 2010-01-01; the first is 2010-01-04) has 2501 changes (n_test).
• Data issues are listed in data_issues:
  • Changes after a holiday span more than one trading session. As the task prescribes, they were kept and attributed to the weekday of t.
  • Crisis-period moves are extreme (for example −51 bp on 2009-03-18). They were kept.
  • Yields are quoted on a 1 bp grid.
• No values were trimmed or winsorised.

# Method

• Joint test (i). Classical one-way equal-variance ANOVA of Δy on weekday, over all 5001 changes, with an F(4, 4996) reference distribution (scipy f_oneway). It was cross-checked against the overall F from an OLS regression on weekday dummies.
• Monday contrast (ii). Difference in means with a Welch two-sample t interval (unequal variances, Welch–Satterthwaite df).
• Out-of-sample comparison (iii). The model forecast for each evaluation-period change is the estimation-period mean change of its weekday (train_weekday_means_bp). The baseline forecast is 0. Both are scored by RMSE over the evaluation period. No evaluation-period information enters the forecasts.
• Conclusion rule. Use the ANOVA at 5%. If it rejects, the sign comes from the Monday interval.
• Robustness checks (extra keys, not part of the decision rule):
  • Monday-indicator OLS with HC1 and Newey–West (5 lags) intervals;
  • Kruskal–Wallis test;
  • Levene test for equal variances;
  • ANOVA excluding the 2008-09 to 2009-06 crisis window.
• Outputs and reproducibility. out/table1.csv and out/figure1.png (weekday means with 95% t-intervals) are produced by out/analysis.py. No randomness is used (random_seed = null).

# Results

• Joint test. ANOVA F = 0.263 (anova_f_stat), p = 0.90 (anova_p_value). Equality of the five weekday means is not rejected.
• Monday contrast. +0.05 bp (effect_estimate), 95% Welch CI [−0.32, +0.42] bp (effect_ci_low, effect_ci_high). This is small next to the typical daily move (evaluation-period RMSE of about 4.9 bp, baseline_metric), and it is not distinguishable from zero.
• Weekday means. All five lie within about ±0.22 bp of zero; every 95% bar in figure 1 covers zero (out/table1.csv).
• Out of sample. The weekday-mean forecast has RMSE 4.884 bp (model_metric), against 4.876 bp for the zero-change forecast (baseline_metric), a ratio of 1.0017 (rmse_ratio_model_over_baseline). Weekday-specific means estimated in 2000–2009 slightly worsen forecasts for 2010–2019.
• Conclusion: no_detectable_effect (conclusion). Over this period, the weekday carries no detectable predictive content for daily 10-year yield changes.

# Uncertainty

• The Monday contrast is pinned down to within about ±0.37 bp (half-width of [effect_ci_low, effect_ci_high]). Weekday effects larger than about 0.4 bp per day on Mondays are therefore inconsistent with these data, but smaller ones cannot be ruled out.
• The Welch interval agrees with the HC1 interval (robust_effect_ci_hc1) and with the Newey–West(5) interval, which allows for short serial correlation (robust_effect_ci_nw5).
• The rank-based Kruskal–Wallis test also does not reject (robust_kruskal_wallis_p = 0.47).
• Excluding the 2008–09 crisis window (4794 changes, n_excl_crisis), the ANOVA still does not reject (robust_anova_p_excl_crisis_2008_09_to_2009_06 = 0.59).
• The out-of-sample RMSE difference was not given a formal test (for example Diebold–Mariano). The 0.17% gap is descriptive only.

# Limitations and open issues

• Equal-variance assumption is violated. Levene's test strongly rejects equal weekday variances (robust_levene_p ≈ 1e-7). The prescribed classical ANOVA p-value is therefore approximate. Heteroskedasticity-robust alternatives (robust_effect_ci_hc1, robust_kruskal_wallis_p) lead to the same conclusion, but a Welch-type ANOVA for the joint test was not computed.
• Dependence and volatility clustering. The ANOVA and Welch tests assume independent observations. Daily yield changes show strong volatility clustering, especially in 2008–09. Only the Monday contrast was given a HAC check (robust_effect_ci_nw5); the joint test was not made HAC-robust.
• Holiday-spanning changes. Changes after a holiday cover two sessions and are attributed to the weekday of t (mostly Tuesdays after Monday holidays). This mixes a calendar-gap effect into the weekday comparison. Excluding or rescaling these changes was not examined.
• Weekend changes. A Monday change spans the weekend (3 calendar days). The data cannot separate weekend news from a genuine Monday effect.
• Low power for tiny effects and non-stationarity. With daily standard deviations of about 5–6 bp, effects of a few tenths of a bp are hard to detect. Weekday patterns could also exist in sub-periods (for example around announcement-heavy days such as payroll Fridays or FOMC Wednesdays) and average out over 20 years. No sub-period or event-day analysis was done beyond the crisis exclusion.
• Narrow out-of-sample test. The comparison uses a single fixed split (2000–2009 vs 2010–2019). Rolling or expanding re-estimation and formal forecast-comparison tests were not done.
• Data revisions and other maturities. FRED vintage effects and other maturities were not checked; the analysis uses only the given file.
• What would overturn the result. A data error in the file (none detected in the audit), or a different definition of the change (for example per-session changes), could alter the result. The conclusion applies only to the stated estimands under the task's definitions.