1# F6-conf-01 — Day-of-week effects in daily 10-year Treasury yield changes23## Question4Using daily FRED DGS10 data for 2000–2019, does the weekday help predict the one-day change in the 10-year Treasury yield, Δy_t = 100·(y_t − y_{t−1}) in basis points? We look at three things: (i) a joint test that the five weekday means are equal; (ii) the Monday contrast (mean on Mondays minus mean on the other weekdays) with a 95% CI; (iii) whether forecasting each change with its weekday mean improves out-of-sample RMSE over a zero-change forecast.56## Data and exclusions7- `data/DGS10.csv`: 5,217 rows (every weekday from 2000-01-03 to 2019-12-31). There are no duplicate dates, the dates are in increasing order, and each weekday appears 1,043–1,044 times. Values range from 1.37% to 6.79%, which is plausible.8- 215 rows have an empty `DGS10` field (market holidays). As the task prescribes, these were dropped before differencing. That leaves 5,002 levels and 5,001 changes (`n_analysed`).9- Estimation period (changes dated ≤ 2009-12-31): n_train = 2,500. Evaluation period (≥ 2010-01-01): n_test = 2,501.10- Data issue: 214 changes span a holiday gap, not counting the ordinary Friday→Monday weekend. Each of these covers more than one business day; most are Tuesdays after a Monday holiday. Following the task rules, they were kept and attributed to the weekday of t. As a result, there are fewer Mondays (919) than other weekdays (1,012–1,030).1112## Method13- Baseline: a zero-change (random-walk) forecast.14- (i) Classical one-way equal-variance ANOVA F-test over all 5,001 changes, using F(4, 4996).15- (ii) Monday contrast: the Monday mean minus the pooled mean of Tuesday–Friday. The 95% interval is a **Welch** two-sample t interval, which allows unequal variances; Welch–Satterthwaite df ≈ 1549.16- (iii) Out-of-sample: each evaluation-period change is forecast by the mean change for its weekday, estimated from 2000–2009 only. RMSE is compared with the zero-change forecast over 2010–2019.17- Supplementary checks, not part of the decision rule: a Diebold–Mariano test on squared loss, Levene's test for equal variances, a Kruskal–Wallis test, and an unconditional training-mean forecast.18- The conclusion follows the task's decision rule: ANOVA at 5%, with the sign taken from the Monday interval if the ANOVA rejects.19- No randomness is involved, so no seed is set. `out/analysis.py` regenerates every number.2021## Results22Table 1 (`out/table1.csv`) gives the mean change by weekday over all changes. Figure 1 (`out/figure1.png`) plots these means with 95% CIs.2324| weekday | n | mean (bp) | SE (bp) |25|---|---|---|---|26| Monday | 919 | −0.052 | 0.164 |27| Tuesday | 1028 | −0.220 | 0.177 |28| Wednesday | 1030 | 0.017 | 0.182 |29| Thursday | 1012 | −0.059 | 0.187 |30| Friday | 1012 | −0.147 | 0.190 |3132- **Joint ANOVA:** F = 0.263, p = 0.902. The equal-means hypothesis is not rejected.33- **Monday contrast:** +0.050 bp, 95% Welch CI [−0.319, +0.420] bp (p = 0.79). This is indistinguishable from zero. It is also economically negligible next to a daily standard deviation of roughly 5 bp.34- **Out-of-sample:** the zero-change RMSE is 4.876 bp. The weekday-mean RMSE is 4.884 bp, so it is slightly *worse*. The Diebold–Mariano statistic is +1.86 (p = 0.063), pointing toward worse but not significant at 5%. An unconditional training-mean forecast gives 4.875 bp.35- **Conclusion code:** `no_detectable_effect`. The weekday carries no detectable predictive content for daily changes in the 10-year yield over 2000–2019.3637## Uncertainty38- The SEs of the weekday means are about 0.16–0.19 bp. The Monday-contrast CI is about ±0.37 bp wide, so any true Monday effect larger than roughly 0.4 bp per day in absolute value is unlikely under the model's assumptions.39- The ANOVA assumes equal variances, and Levene's test rejects that assumption (p ≈ 1e-7). The Welch interval for the contrast does not rely on the assumption.40- The rank-based Kruskal–Wallis test also finds no difference (p = 0.52), so the null result does not depend on normality or equal variances.41- The intervals treat daily changes as independent. Daily yield changes have little autocorrelation but strong volatility clustering. HAC standard errors were not computed, but they would most likely widen the intervals somewhat and would not overturn a result with p ≈ 0.9.4243## Limitations and open issues44- **What would invalidate the result:**45 - Strong serial dependence or volatility clustering that makes the iid SEs badly wrong. This is a concern for inference in general, but it cannot manufacture a rejection here; it could only mask a small effect.46 - A data-revision or vintage problem in the FRED series. This was not checked: only one vintage was available, and we cannot verify the SHA beyond what the README states.47- **Holiday-spanning changes:** these mix one-day and multi-day changes. Under the prescribed rule they are attributed to the weekday of t, which mostly inflates Tuesday variance. A per-business-day normalisation or excluding these changes was not tried.48- **Not checked:**49 - Sub-period stability, e.g. 2008 crisis versus calm periods, or the pre/post-2010 weekday means separately beyond the training means.50 - Interaction with macro-announcement days. Employment reports fall on Fridays and FOMC decisions mid-week, so any weekday pattern could reflect an announcement calendar rather than the weekday itself.51 - Robust or median-based contrasts, and HAC or GARCH-adjusted inference.52- **Power:** with about 1,000 observations per weekday and a daily SD of about 5 bp, effects smaller than about 0.4–0.5 bp cannot be detected. "No detectable effect" therefore does not mean "exactly zero".53- **Multiple comparisons and folklore:** the Monday contrast was pre-specified by the task. Any other weekday contrast singled out from Table 1 (e.g. Tuesday's −0.22 bp) would be data-mined and is not significant anyway.54- **Generality:** the result covers one maturity, one 20-year window and the mean only. It says nothing about weekday patterns in volatility, which Levene's test suggests do exist.55