# Day-of-week effects in daily changes of the 10-year Treasury yield (F6-conf-01)

# Question

Does the weekday predict the one-day change Δy_t (basis points) in the 10-year US Treasury constant-maturity yield (FRED DGS10), 2000–2019? The three estimands are: (i) a joint test of equal weekday means; (ii) the Monday contrast (mean change on Mondays minus the mean on Tuesday–Friday) with a 95% interval; (iii) the out-of-sample RMSE of a forecast from weekday-specific means, compared with a zero-change (random-walk) forecast.

# Data and exclusions

data/DGS10.csv has 5217 rows (n_input_rows), and its SHA-256 matches the README (input_sha256). 215 rows have an empty yield field because of US market holidays (n_missing_rows); they are dropped. Removing the first available observation, which has no change, leaves 5001 daily changes (n_analysed), dated first_change_date (2000-01-04) to last_change_date (2019-12-31). Of these, 2500 fall 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. There are no duplicated dates, no weekend dates and no non-numeric values. The largest moves are genuine: −51 bp on 2009-03-18 (diag_dy_min_bp) and +25 bp on 2001-11-15 (diag_dy_max_bp).

# Method

• Δy_t = 100·(y_t − y_{t−1}), taken between consecutive available observations and attributed to the weekday of t. This follows the task rule, so a change after a holiday covers more than one trading day.
• (i) Classical one-way ANOVA F-test (equal variances) of the five weekday means, using all 5001 changes, with reference distribution F(4, 4996).
• (ii) Monday contrast: Welch two-sample t interval (unequal variances; Welch df in effect_welch_df). This was chosen because weekday variances differ (see Uncertainty).
• (iii) The forecast for each evaluation-period change is the estimation-period mean change for its weekday (train_weekday_means_bp). It is compared with a zero-change forecast by RMSE over 2010–2019. Nothing from the evaluation period enters the forecast.
• Decision rule: if the ANOVA has p ≥ 0.05 the conclusion is no_detectable_effect; otherwise the sign is taken from the Monday interval.
• Sensitivity checks reported below: OLS with HC1 robust SE, pooled-variance interval, Kruskal–Wallis test, ANOVA excluding post-holiday changes, and ANOVA separately for each period. The analysis uses no randomness (random_seed = null). Outputs are out/figure1.png and out/table1.csv.

# Results

• Weekday means are all within about ±0.22 bp of zero (Tuesday −0.22, Wednesday +0.02, Friday −0.15; see out/table1.csv and out/figure1.png). By comparison, the daily standard deviation is 5.72 bp (diag_dy_sd_bp).
• Joint test: 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 (2010–2019): zero-change RMSE 4.8757 bp (baseline_metric); weekday-mean RMSE 4.8838 bp (model_metric). The weekday model is slightly worse, by 0.008 bp (model_minus_baseline_rmse).
• Conclusion: no_detectable_effect (conclusion). In this sample, the weekday has no detectable in-sample or out-of-sample predictive content for daily 10-year yield changes.

# Uncertainty

• The Monday interval is about ±0.37 bp wide (effect_se = 0.188). Any Monday effect larger than about 0.4 bp in absolute value is therefore inconsistent with the data. This is small compared with the 5.7 bp daily volatility.
• The result holds across the checks: HC1 regression CI [−0.319, 0.419] (robust_mon_hc1_ci); pooled CI [−0.360, 0.460] (robust_mon_pooled_ci); Kruskal–Wallis p = 0.52 (robust_kruskal_p); ANOVA without the 155 post-holiday changes (n = 4846, robust_n_excl_post_holiday) p = 0.85 (robust_anova_p_excl_post_holiday); ANOVA p = 0.73 in 2000–2009 (robust_anova_p_train) and 0.33 in 2010–2019 (robust_anova_p_test).
• Monday's training-period mean (−0.05 bp) and the training means for other days, which ranged from −0.41 to +0.12 bp (train_weekday_means_bp), did not carry over out of sample. This is consistent with them being noise.
• The RMSE difference (0.008 bp) has no interval attached; no Diebold–Mariano test was run. It is not evidence of a real difference in either direction.

# Limitations and open issues

• Assumption violation: Weekday variances differ significantly (Levene p ≈ 1e-7, diag_levene_p). Monday changes are the least volatile (sd 4.98 vs 6.04 bp on Friday, diag_sd_by_weekday_bp). The classical equal-variance ANOVA required by the task is therefore misspecified in its variance assumption. The Welch, HC1 and rank-based checks agree with it, but a heteroskedasticity-robust joint test (e.g. Welch ANOVA) was not computed. The weekday pattern in volatility is a real feature of the data. It is outside the mean-change estimand and was not studied further.
• Dependence and fat tails: Lag-1 autocorrelation is negligible (−0.008, diag_lag1_autocorr). Volatility clustering (GARCH-type dependence) and fat tails were not modelled. They could make the iid-based standard errors somewhat optimistic, but with p = 0.90 this would not change the conclusion.
• Definition choices: Changes after a holiday cover several days but are attributed to a single weekday (task rule). Excluding them does not change the result. Rounding the series to 2 decimals (1 bp resolution) is negligible next to the 5.7 bp volatility.
• What would invalidate the result: a wrong weekday assignment (checked: every date is a weekday); look-ahead in the forecast (checked: training means use only changes ≤2009-12-31); or a weekday effect confined to sub-periods or regimes (e.g. FOMC or data-release days, which cluster on certain weekdays). Sub-period instability was checked only with the two-period split. Calendar-event confounding was not checked.
• Power: Absence of evidence is not proof of zero. Effects smaller than about 0.3–0.4 bp/day cannot be ruled out, but they would be economically trivial relative to daily volatility and to transaction costs.
• Scope: These conclusions apply to the 10-year CMT yield, 2000–2019, only. Other maturities, other periods and intraday data were not examined.