# 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) a joint test of equal weekday means; (ii) the Monday contrast (Monday mean minus mean of other weekdays) with a 95% CI; (iii) out-of-sample RMSE of weekday-specific means vs. a zero-change (random-walk) forecast.

# Data and exclusions

• data/DGS10.csv: 5,217 weekday rows (header excluded), 2000-01-03 … 2019-12-31.
• 215 rows have an empty DGS10 field (US market holidays); they were dropped first, as required. No non-numeric values, duplicated dates or weekend rows were found (checked in code).
• Changes Δy_t = 100·(y_t − y_{t−1}) between consecutive available observations: 5,001 changes (first observation has no change). Estimation period (≤ 2009-12-31): n_train = 2,500; evaluation period (≥ 2010-01-01): n_test = 2,501.
• 214 changes span a holiday gap (e.g. the Tuesday after a Monday holiday covers Friday→Tuesday). They are kept and attributed to the weekday of their end date, per the task rules.

# Method

• Joint test: classical one-way equal-variance ANOVA F-test of equal weekday means on all 5,001 changes, F(4, 4996).
• Monday contrast: difference of sample means (Monday vs. all other weekdays pooled), with a Welch two-sample t interval (unequal variances, Welch–Satterthwaite df).
• Out-of-sample: weekday means estimated on the estimation period only, used to forecast each evaluation-period change; compared to the zero-change forecast by RMSE (bp). No randomness is involved (no seed).
• Decision rule: ANOVA at 5%; only if it rejects is the sign taken from the Monday-contrast CI.

# Results

(Table: out/table1.csv; figure: out/figure1.png.)

• 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).
• Out-of-sample (2010–2019): zero-change RMSE = 4.876 bp; weekday-mean RMSE = 4.884 bp (ratio 1.0017). Weekday-specific means slightly worsen forecasts relative to the random walk.
• Conclusion: no_detectable_effect. Over 2000–2019 the day of the week has no detectable in-sample or out-of-sample predictive content for daily 10-year yield changes.

# Uncertainty

The weekday means are all within about ±0.25 bp of zero, while the daily standard deviation is about 5 bp; the standard errors (~0.16–0.19 bp) are comparable to or larger than the means. The Monday-contrast CI half-width is ≈0.37 bp, so Monday effects larger than roughly ±0.4 bp/day can be ruled out at 95% confidence (under the i.i.d.-type assumptions of the Welch interval), but smaller effects cannot be. The RMSE difference (0.008 bp) is tiny; no formal forecast-comparison test (e.g. Diebold–Mariano) was run, so we do not claim the weekday model is significantly worse, only that it is not better.

# Limitations and open issues

• Dependence and heteroskedasticity: daily yield changes show volatility clustering (e.g. 2008–09, 2013 taper tantrum). The ANOVA assumes equal variances and independence; the Welch interval allows unequal group variances but not serial correlation or time-varying volatility. HAC-based inference was not run; it could change p-values somewhat, but with F ≈ 0.26 a reversal to significance is implausible.
• Holiday-spanning changes: 214 changes cover more than the normal horizon and are concentrated on Tuesdays/Fridays/Mondays adjacent to holidays; this mixes horizons across weekdays. A sensitivity analysis excluding them was not performed.
• Weekend horizon: Monday changes cover three calendar days, so a variance difference (not a mean difference) would be expected; we tested means only, not variances.
• Non-stationarity: the 2000–2019 period has a strong downward yield trend (≈−0.09 bp/day on average, from 6.58% to 1.92%) and regime changes (ZLB, QE); weekday effects could exist within sub-periods and cancel overall. Sub-period stability was not checked beyond the train/test split.
• Multiple testing / specification: only the Monday contrast was examined as a specific contrast; other contrasts (e.g. Friday) were not pre-specified and were not tested.
• What would invalidate the result: errors in the source data (FRED revisions), or a different change definition (e.g. dropping holiday-gap changes) materially altering means — unlikely given the size of the SEs relative to the means, but unchecked.
• External validity: results concern the 10y CMT yield in 2000–2019 only; not other maturities, assets or periods.