# 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 = 100·(y_t − y_{t−1}) (bp) in the 10-year constant-maturity Treasury 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 weekday-mean forecasts vs a zero-change random-walk forecast.

# Data and exclusions

• data/DGS10.csv: 5217 rows (all weekdays 2000-01-03 … 2019-12-31). 215 rows have an empty DGS10 field (market holidays) and were dropped, leaving 5002 yields and 5001 changes.
• No non-numeric values, duplicated dates, unsorted dates or weekend dates were found (checked in code).
• Changes are computed between consecutive available observations and attributed to the weekday of t; 214 changes span a holiday gap (e.g. Tuesday after a Monday holiday) and are kept as specified.
• Estimation period (≤ 2009-12-31): n_train = 2500 changes; evaluation period (≥ 2010-01-01): n_test = 2501.

# Method

• Joint test: classical equal-variance one-way ANOVA F-test (scipy f_oneway) on all 5001 changes, F(4, 4996).
• Monday contrast: OLS of Δy on a constant and a Monday indicator; the slope equals mean(Monday) − mean(other days). 95% CI uses HC3 heteroskedasticity-robust SEs (normal critical values). Welch two-sample t-test reported as a cross-check.
• Out-of-sample: each evaluation-period change is forecast by the estimation-period mean change of its weekday; compared with the zero-change forecast by RMSE (bp). Weekday means use only the estimation period.
• Conclusion rule: ANOVA at 5%; if it rejected, sign taken from the Monday-contrast CI. No randomness is involved (no seed).

# Results

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

• ANOVA: F = 0.263, p = 0.902 — no evidence that weekday means differ.
• Monday contrast: +0.050 bp, 95% CI [−0.319, 0.420] bp (HC3; Welch p = 0.79).
• Out-of-sample RMSE: zero-change baseline 4.876 bp; weekday-mean model 4.884 bp (ratio 1.0017) — the weekday model is slightly worse than the random walk.
• Conclusion code: no_detectable_effect. Figure 1 (out/figure1.png) shows weekday means with 95% CIs, all overlapping zero.

# Uncertainty

Weekday means have SEs of ~0.16–0.19 bp against a daily standard deviation of ~5–6 bp, so the design can detect only weekday differences of roughly ≥0.5 bp; smaller effects cannot be excluded. The Monday contrast CI (width ~0.74 bp) rules out a Monday effect larger than about ±0.4 bp/day. The RMSE comparison is a single 2010–2019 split without a formal test (e.g. Diebold–Mariano); the 0.17% difference is negligible either way.

# Limitations and open issues

• What would invalidate the result: strong volatility clustering and serial dependence in daily yield changes violate the ANOVA's i.i.d./equal-variance assumptions; heavy tails (crisis days in 2008, 2001) could distort the F-test's size. The HC3 interval addresses heteroskedasticity but not autocorrelation or GARCH-type dependence; a HAC or block-bootstrap check was not done.
• Not checked: subperiod stability of weekday patterns (effects could exist and cancel across regimes); interaction with macro announcement calendars (e.g. payrolls on Fridays, FOMC days on Wednesdays), which are the plausible mechanism behind any weekday pattern; distributional (variance) differences by weekday — only means were tested.
• Measurement threats: holiday-gap changes (214) mix multi-day moves into specific weekdays (notably Tuesdays after Monday holidays); Monday changes span the weekend by construction. H.15 yields are rounded to 0.01 pp (1 bp), coarse relative to the effect sizes considered. FRED data may be revised; results correspond to the bundled file.
• Multiple testing / data-mining: the weekday hypothesis is one of many calendar anomalies; a null here is consistent with the anomaly literature's fragility, but a significant result would have needed out-of-sample corroboration, which the RMSE comparison does not provide.