1# F6-conf-01 — Day-of-week effects in daily changes of the 10-year Treasury yield, 2000–201923## Question4Can the day of the week predict the one-day change in the 10-year US Treasury constant-maturity yield (FRED DGS10)? We estimate (i) a joint test that the mean change is the same on all five weekdays; (ii) the "Monday contrast" (mean Monday change minus mean change on Tuesday–Friday) with a 95% interval; (iii) whether weekday-specific means from 2000–2009 forecast 2010–2019 changes better than a zero-change (random-walk) forecast.56## Data and exclusions7`data/DGS10.csv` has 5217 rows (`n_input_rows`), one per weekday from 2000-01-03 to 2019-12-31. Its SHA-256 matches `data/README.md`. 215 rows have an empty yield field (US market holidays and closures; `n_missing_rows`) and are dropped first. One-day changes Δy_t = 100·(y_t − y_{t−1}) bp are taken between consecutive available observations and assigned to the weekday of t. The first observation has no change. This gives 5001 changes (`n_analysed`): 2500 dated on or before 2009-12-31 (`n_train`) and 2501 dated on or after 2010-01-01 (`n_test`). The exclusion ledger is in `out/exclusions.csv` (5217 − 215 − 1 = 5001). No outliers are removed. The largest move is −51 bp on 2009-03-18 (the FOMC QE announcement), a genuine market move that is kept. Data issues are listed in `data_issues`.89## Method10- Baseline: zero-change forecast. Its RMSE over the evaluation period is `baseline_metric`.11- Joint test: classical equal-variance one-way ANOVA of Δy_t on weekday, using all 5001 changes, with F(4, 4996) (`anova_f_stat`, `anova_p_value`).12- Monday contrast: mean(Monday) − mean(Tue–Fri) over all changes. The 95% interval is a Welch two-sample t interval, chosen because it does not assume equal variances (`effect_estimate`, `effect_ci_low`, `effect_ci_high`; method in `effect_ci_method`).13- Out-of-sample: each 2010–2019 change is forecast by the mean change of its weekday over 2000–2009 only (`train_weekday_means_bp`). This RMSE is `model_metric`. As a supplement, a Diebold–Mariano-type test compares squared-error losses of this forecast and the zero forecast (normal approximation, no HAC correction; `oos_dm_stat_model_vs_zero`, `oos_dm_p_value`).14- Conclusion rule (from TASK): if the ANOVA does not reject at 5%, the code is `no_detectable_effect`; otherwise the sign comes from the Monday interval.15- No randomness is used (`random_seed` = null). `out/analysis.py` regenerates every output deterministically.1617## Results18- Weekday means (table: `out/table1.csv`; figure: `out/figure1.png`) range from about −0.22 bp (Tuesday) to +0.02 bp (Wednesday). Each is within about 1.2 standard errors of zero. A typical daily change has an SD of about 5.7 bp.19- ANOVA: F = 0.263, p = 0.902 (`anova_f_stat`, `anova_p_value`). This gives no evidence that weekday means differ.20- Monday contrast: +0.050 bp, 95% CI [−0.319, +0.420] bp (`effect_estimate`, `effect_ci_low`, `effect_ci_high`). Welch p = 0.79 (`effect_welch_p_value`).21- Out-of-sample RMSE: zero-change forecast 4.876 bp (`baseline_metric`), weekday-means forecast 4.884 bp (`model_metric`). The weekday forecast is slightly worse; the RMSE ratio is 1.0017 (`oos_rmse_ratio_model_to_baseline`). The DM-type test gives stat = 1.86, p = 0.063 (`oos_dm_stat_model_vs_zero`, `oos_dm_p_value`). Weekday means estimated in 2000–2009 did not improve forecasts in 2010–2019.22- Conclusion code: `no_detectable_effect` (`conclusion`).2324## Uncertainty25The Monday-contrast interval is narrow in absolute terms: it is about ±0.37 bp, roughly 6% of one daily SD. It rules out Monday effects larger than about 0.4 bp per day in either direction (`effect_ci_low`, `effect_ci_high`, `effect_se`). The ANOVA p-value of 0.90 is far from any conventional threshold. The out-of-sample RMSE difference is 0.008 bp, which is negligible in magnitude. Its sign (weekday means are worse) is what we would expect when noisy in-sample means are used as forecasts and the true effect is absent.2627## Limitations and open issues28- **What could invalidate the result.** Both the ANOVA and the Welch interval assume independent observations. Daily yield changes show volatility clustering (conditional heteroskedasticity), heavy tails, and some weak autocorrelation. The ANOVA also assumes equal variances across weekdays. If variance differs by weekday (for example, on days with employment reports, which are mostly Fridays), the classical F-test can be miscalibrated. With such small F, it is unlikely that a corrected test would reject, but we did **not** run HAC, robust-ANOVA (Welch/Brown–Forsythe), or bootstrap checks.29- **Definition effects.** Changes after holidays span more than one trading day; for example, the Tuesday after a Monday holiday covers a long weekend. Following the TASK definition, these are attributed to the weekday of t, which mixes "post-holiday" and weekday effects. Monday changes also always span a weekend. We did not separate these.30- **Regime changes.** The sample includes the 2008–09 crisis, QE, and the zero-lower-bound era. Weekday patterns may vary over time; a null over 20 years does not rule out effects in sub-periods, which we did not test. The out-of-sample comparison uses a single split rather than a rolling evaluation.31- **Not checked.** Other maturities, intraday timing, announcement-day effects, and a power analysis for effects smaller than the CI half-width. Data are taken as published by FRED (H.15); revisions or errors in the source were not checked.32- **Multiple testing.** Only the Monday contrast was pre-specified. The other pairwise weekday differences were not tested, which avoids a multiple-comparison problem.33