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

# Question

Does the weekday carry predictive content for the one-day change Δy_t (bp) in the 10-year US Treasury constant-maturity yield (FRED DGS10), 2000–2019? Estimands: (i) joint equality of the five weekday means (one-way ANOVA); (ii) the Monday contrast (Monday mean minus mean of other weekdays) with a 95% CI; (iii) out-of-sample RMSE of estimation-period weekday means vs a zero-change (random-walk) forecast.

# Data and exclusions

• data/DGS10.csv: 5,217 rows read (header excluded), every weekday 2000-01-03 … 2019-12-31.
• 215 rows have an empty DGS10 field (US market holidays) and were dropped first, as required. No non-numeric values, duplicate dates or weekend dates were found.
• Δy_t = 100·(y_t − y_{t−1}) between consecutive available observations, attributed to the weekday of t; the first observation has no change → 5,001 changes (all used in the ANOVA).
• Estimation period (≤ 2009-12-31): 2,500 changes; evaluation period (≥ 2010-01-01): 2,501 changes.
• 214 changes span a holiday gap (e.g. Tuesday after a Monday holiday, covering two business days). They are kept, as the task definition prescribes, and flagged as a limitation.

# Method

• Baseline: zero-change forecast (random walk in levels), RMSE over the evaluation period.
• Joint test: classical equal-variance one-way ANOVA F-test (scipy f_oneway) of equal weekday means over all 5,001 changes, F(4, 4996).
• Monday contrast: mean Monday change minus mean change over Tue–Fri pooled, all changes; 95% CI from a Welch two-sample t interval (unequal variances, Welch–Satterthwaite df).
• Out-of-sample model: each evaluation-period change is forecast by the estimation-period (2000–2009) mean change of its weekday; RMSE compared to the baseline. A descriptive Diebold–Mariano statistic (squared loss) is reported as supplementary.
• Conclusion rule: ANOVA at 5%; if it rejected, the sign would come from the Monday-contrast interval. No randomness is used (random_seed = null).

# Results

Table 1 (out/table1.csv), all changes:

Figure 1 (out/figure1.png) plots these means with 95% CIs; all intervals cover zero and overlap heavily.

• ANOVA: F = 0.263, p = 0.902 → no evidence that weekday means differ.
• Monday contrast: +0.050 bp, 95% Welch CI [−0.319, +0.420] bp (Welch p = 0.79). The daily change has SD ≈ 5.7 bp, so this is tiny and indistinguishable from zero.
• Out-of-sample (2010–2019): zero-change RMSE = 4.876 bp; weekday-mean RMSE = 4.884 bp. The weekday model is slightly worse than the random-walk baseline (DM statistic −1.86, p ≈ 0.063, favouring the baseline at the margin).
• Conclusion code: no_detectable_effect.

# Uncertainty

The Monday-contrast CI half-width is about 0.37 bp, so effects larger than roughly ±0.4 bp/day on Mondays relative to other days are ruled out at 95% under the stated assumptions. The weekday SEs (~0.16–0.19 bp) are about 30 times smaller than the daily SD, yet no mean is distinguishable from zero. The ANOVA assumes equal variances and independence; the Welch interval relaxes only equal variance. The out-of-sample RMSE gap (0.008 bp) is very small relative to the RMSE level, and its DM p-value is only marginal; the direction (in-sample weekday means do not help out of sample) is the robust takeaway, not its exact size.

# Limitations and open issues

• What would invalidate the result: strong serial dependence or volatility clustering in Δy_t (clearly present in rates data, e.g. 2008–2009) makes the classical ANOVA's i.i.d., equal-variance assumptions wrong; this mostly affects SEs/p-values. Given that F is far below 1 and p ≈ 0.90, a plausible correction would be unlikely to produce rejection, but a HAC/heteroskedasticity-robust Wald test was not run.
• Holiday-spanning changes: 214 changes cover more than one business day and are attributed to the post-holiday weekday (often Tuesday), mixing two days of news and inflating that weekday's variance. Not re-analysed with these excluded.
• Fat tails: daily yield changes are heavy-tailed; means are sensitive to a few large moves (e.g. crisis days). No robust (median/trimmed) analysis or permutation test was performed.
• Regime dependence: the effect could exist in sub-periods (e.g. pre-2008 vs zero-lower-bound years) and cancel in aggregate; sub-period stability was not checked beyond the single train/test split.
• Multiple comparisons / specification: only a Monday contrast was pre-specified; individual weekday-vs-rest comparisons (e.g. Tuesday's −0.22 bp) were not tested and should not be over-read.
• Data: DGS10 is a fitted constant-maturity yield rounded to 0.01%, not a traded price; FRED vintages can be revised. Only one maturity was examined, so the result says nothing about other tenors or about intraday/weekend-news timing effects.
• The out-of-sample comparison uses a single split and RMSE only; economic (trading) value was not evaluated.