# F6-conf-01 — Weekday effects in daily changes of the 10-year Treasury yield

## Question
Does the day of the week help predict the one-day change Δy_t (basis points) in the 10-year US Treasury constant-maturity yield (FRED DGS10) over 2000–2019? There are three estimands: (i) a joint test that the five weekday means are equal; (ii) the Monday contrast (mean on Mondays minus mean on Tuesday–Friday), with a 95% interval; (iii) the out-of-sample RMSE of weekday-mean forecasts against a zero-change forecast.

## Data and exclusions
- Input: `data/DGS10.csv`, 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 because of US market holidays, including the 2001-09-11/12 closure (`n_missing_rows`). These rows were dropped first. One more observation was lost because the first available observation has no change. This leaves 5001 daily changes (`n_analysed`), see `out/exclusions.csv`.
- The estimation period (changes dated ≤ 2009-12-31) has 2500 changes (`n_train`). The evaluation period (changes dated ≥ 2010-01-01; the first is 2010-01-04) has 2501 changes (`n_test`).
- Data issues are listed in `data_issues`:
  - Changes after a holiday span more than one trading session. As the task prescribes, they were kept and attributed to the weekday of t.
  - Crisis-period moves are extreme (for example −51 bp on 2009-03-18). They were kept.
  - Yields are quoted on a 1 bp grid.
- No values were trimmed or winsorised.

## Method
- **Joint test (i).** Classical one-way equal-variance ANOVA of Δy on weekday, over all 5001 changes, with an F(4, 4996) reference distribution (scipy `f_oneway`). It was cross-checked against the overall F from an OLS regression on weekday dummies.
- **Monday contrast (ii).** Difference in means with a **Welch** two-sample t interval (unequal variances, Welch–Satterthwaite df).
- **Out-of-sample comparison (iii).** The model forecast for each evaluation-period change is the estimation-period mean change of its weekday (`train_weekday_means_bp`). The baseline forecast is 0. Both are scored by RMSE over the evaluation period. No evaluation-period information enters the forecasts.
- **Conclusion rule.** Use the ANOVA at 5%. If it rejects, the sign comes from the Monday interval.
- **Robustness checks (extra keys, not part of the decision rule):**
  - Monday-indicator OLS with HC1 and Newey–West (5 lags) intervals;
  - Kruskal–Wallis test;
  - Levene test for equal variances;
  - ANOVA excluding the 2008-09 to 2009-06 crisis window.
- **Outputs and reproducibility.** `out/table1.csv` and `out/figure1.png` (weekday means with 95% t-intervals) are produced by `out/analysis.py`. No randomness is used (`random_seed` = null).

## Results
- **Joint test.** ANOVA F = 0.263 (`anova_f_stat`), p = 0.90 (`anova_p_value`). Equality of the five weekday means is not rejected.
- **Monday contrast.** +0.05 bp (`effect_estimate`), 95% Welch CI [−0.32, +0.42] bp (`effect_ci_low`, `effect_ci_high`). This is small next to the typical daily move (evaluation-period RMSE of about 4.9 bp, `baseline_metric`), and it is not distinguishable from zero.
- **Weekday means.** All five lie within about ±0.22 bp of zero; every 95% bar in figure 1 covers zero (`out/table1.csv`).
- **Out of sample.** The weekday-mean forecast has RMSE 4.884 bp (`model_metric`), against 4.876 bp for the zero-change forecast (`baseline_metric`), a ratio of 1.0017 (`rmse_ratio_model_over_baseline`). Weekday-specific means estimated in 2000–2009 slightly *worsen* forecasts for 2010–2019.
- **Conclusion:** `no_detectable_effect` (`conclusion`). Over this period, the weekday carries no detectable predictive content for daily 10-year yield changes.

## Uncertainty
- The Monday contrast is pinned down to within about ±0.37 bp (half-width of [`effect_ci_low`, `effect_ci_high`]). Weekday effects larger than about 0.4 bp per day on Mondays are therefore inconsistent with these data, but smaller ones cannot be ruled out.
- The Welch interval agrees with the HC1 interval (`robust_effect_ci_hc1`) and with the Newey–West(5) interval, which allows for short serial correlation (`robust_effect_ci_nw5`).
- The rank-based Kruskal–Wallis test also does not reject (`robust_kruskal_wallis_p` = 0.47).
- Excluding the 2008–09 crisis window (4794 changes, `n_excl_crisis`), the ANOVA still does not reject (`robust_anova_p_excl_crisis_2008_09_to_2009_06` = 0.59).
- The out-of-sample RMSE difference was not given a formal test (for example Diebold–Mariano). The 0.17% gap is descriptive only.

## Limitations and open issues
- **Equal-variance assumption is violated.** Levene's test strongly rejects equal weekday variances (`robust_levene_p` ≈ 1e-7). The prescribed classical ANOVA p-value is therefore approximate. Heteroskedasticity-robust alternatives (`robust_effect_ci_hc1`, `robust_kruskal_wallis_p`) lead to the same conclusion, but a Welch-type ANOVA for the joint test was not computed.
- **Dependence and volatility clustering.** The ANOVA and Welch tests assume independent observations. Daily yield changes show strong volatility clustering, especially in 2008–09. Only the Monday contrast was given a HAC check (`robust_effect_ci_nw5`); the joint test was not made HAC-robust.
- **Holiday-spanning changes.** Changes after a holiday cover two sessions and are attributed to the weekday of t (mostly Tuesdays after Monday holidays). This mixes a calendar-gap effect into the weekday comparison. Excluding or rescaling these changes was not examined.
- **Weekend changes.** A Monday change spans the weekend (3 calendar days). The data cannot separate weekend news from a genuine Monday effect.
- **Low power for tiny effects and non-stationarity.** With daily standard deviations of about 5–6 bp, effects of a few tenths of a bp are hard to detect. Weekday patterns could also exist in sub-periods (for example around announcement-heavy days such as payroll Fridays or FOMC Wednesdays) and average out over 20 years. No sub-period or event-day analysis was done beyond the crisis exclusion.
- **Narrow out-of-sample test.** The comparison uses a single fixed split (2000–2009 vs 2010–2019). Rolling or expanding re-estimation and formal forecast-comparison tests were not done.
- **Data revisions and other maturities.** FRED vintage effects and other maturities were not checked; the analysis uses only the given file.
- **What would overturn the result.** A data error in the file (none detected in the audit), or a different definition of the change (for example per-session changes), could alter the result. The conclusion applies only to the stated estimands under the task's definitions.