5-year Treasury Yield
Linear model of 5-year Treasury Yield at period t from the other tracked series and the LN_ / squared transforms described on the Regression Models index: Y(t) = Σ ai Xi(t−6).
Integrated series (S&P 500, Dow, Home Price Index, Commercial RE) are fit as ΔY. Quarterly series use one row per quarter.
Terms are added one at a time to minimize training AIC, at most min(5, n/8) predictors, one transform per driver, and only when the term’s p-value is at most 0.1 and |coefficient| is greater than 1.0e-10. A candidate correlated above 0.8 with Y or with an already selected X is skipped.
LN_ and squared predictors are clamped to their training range. Coefficients smaller than 0.001 are shown in scientific notation.
Each section is one quarter in a one-year walk (4 experiments). The newest label is the current quarter (3Q2026). The test window is the prior 6 quarters of Y; the train window is the five years (20 quarters) before that. Independents are two quarters (six months) older than Y. Dates on this page are quarter-end observations.
Charts start in January 2020 and plot published prints only (not carried-forward extra samples). Fitted (train), fitted (test), and forecast are joined at the window boundaries so the line is continuous through the label quarter. The OLS test/forecast is shown when its test MAE beats or matches a last-print (or zero-change) baseline.
An intercept-only heading (for example “Δ SP500 = 40.657”) means no lagged series improved training AIC by at least 2 after the intercept, so the model is the training-mean change (a random walk with drift).
Test MAE is omitted when every print in the test window is a CCAR extra sample rather than a published observation.
3Q2026: 5-year Treasury Yield = -37.226 + 0.601 × LN_1-year Treasury Yield + 4.826 × LN_SP500 Stock Price Index
Train: 1Q2020 – 4Q2024 (20 observations). Test: 1Q2025 – 2Q2026 (6 observations). Independents are dated two quarters (six months) before each Y period.
| Dependent variable (+/- SE): | |
| 5-year Treasury Yield | |
| Constant | -37.226 (+/- 6.934) |
| p = 0.0001*** | |
| LN_1-year Treasury Yield | 0.601 (+/- 0.086) |
| p = 0.00001*** | |
| LN_SP500 Stock Price Index | 4.826 (+/- 0.840) |
| p = 0.00003*** | |
| Observations | 20 |
| R2 | 0.876 |
| Adjusted R2 | 0.862 |
| Residual Std. Error | 0.611 (df = 17) |
| F Statistic | 60.248*** (df = 2; 17) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (1Q2025 – 2Q2026)
| MAE | 0.96 |
| Last-print MAE | 0.2 |
| RMSE | 0.984 |
| R2 | -21.767 |
Chart forecast uses the last-print baseline (OLS MAE is worse).
R2 impact
Train ΔR2 is the gain when the term was added. Test ΔR2 is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.
| Variable | Train ΔR2 | Test ΔR2 |
|---|---|---|
| LN_1-year Treasury Yield | +0.6365 | -21.3085 |
| LN_SP500 Stock Price Index | +0.2398 | +38297.7556 |
2Q2026: 5-year Treasury Yield = 0.274 + 0.13 × 6-month Treasury Yield² + 0.032 × CPI Inflation Rate²
Train: 4Q2019 – 3Q2024 (20 observations). Test: 4Q2024 – 1Q2026 (6 observations). Independents are dated two quarters (six months) before each Y period.
| Dependent variable (+/- SE): | |
| 5-year Treasury Yield | |
| Constant | 0.274 (+/- 0.186) |
| p = 0.159 | |
| 6-month Treasury Yield2 | 0.130 (+/- 0.009) |
| p = 0.000*** | |
| CPI Inflation Rate2 | 0.032 (+/- 0.004) |
| p = 0.00000*** | |
| Observations | 20 |
| R2 | 0.930 |
| Adjusted R2 | 0.922 |
| Residual Std. Error | 0.451 (df = 17) |
| F Statistic | 113.180*** (df = 2; 17) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (4Q2024 – 1Q2026)
| MAE | 0.9 |
| Last-print MAE | 0.2 |
| RMSE | 0.98 |
| R2 | -21.583 |
Chart forecast uses the last-print baseline (OLS MAE is worse).
R2 impact
Train ΔR2 is the gain when the term was added. Test ΔR2 is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.
| Variable | Train ΔR2 | Test ΔR2 |
|---|---|---|
| 6-month Treasury Yield² | +0.6313 | +256.2808 |
| CPI Inflation Rate² | +0.2988 | +10.8474 |
1Q2026: 5-year Treasury Yield = -0.042 + 0.731 × 6-month Treasury Yield + 0.031 × CPI Inflation Rate²
Train: 3Q2019 – 2Q2024 (20 observations). Test: 3Q2024 – 4Q2025 (6 observations). Independents are dated two quarters (six months) before each Y period.
| Dependent variable (+/- SE): | |
| 5-year Treasury Yield | |
| Constant | -0.042 (+/- 0.184) |
| p = 0.822 | |
| 6-month Treasury Yield | 0.731 (+/- 0.049) |
| p = 0.000*** | |
| CPI Inflation Rate2 | 0.031 (+/- 0.003) |
| p = 0.00000*** | |
| Observations | 20 |
| R2 | 0.935 |
| Adjusted R2 | 0.928 |
| Residual Std. Error | 0.427 (df = 17) |
| F Statistic | 122.959*** (df = 2; 17) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (3Q2024 – 4Q2025)
| MAE | 0.48 |
| Last-print MAE | 0.3 |
| RMSE | 0.56 |
| R2 | -6.376 |
Chart forecast uses the last-print baseline (OLS MAE is worse).
R2 impact
Train ΔR2 is the gain when the term was added. Test ΔR2 is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.
| Variable | Train ΔR2 | Test ΔR2 |
|---|---|---|
| 6-month Treasury Yield | +0.6357 | +323.2235 |
| CPI Inflation Rate² | +0.2996 | +3.4393 |
4Q2025: 5-year Treasury Yield = -27.452 + 1.891 × LN_10-year Treasury Yield + 3.476 × LN_SP500 Stock Price Index
Train: 2Q2019 – 1Q2024 (20 observations). Test: 2Q2024 – 3Q2025 (6 observations). Independents are dated two quarters (six months) before each Y period.
| Dependent variable (+/- SE): | |
| 5-year Treasury Yield | |
| Constant | -27.452 (+/- 6.970) |
| p = 0.002*** | |
| LN_10-year Treasury Yield | 1.891 (+/- 0.282) |
| p = 0.00001*** | |
| LN_SP500 Stock Price Index | 3.476 (+/- 0.858) |
| p = 0.001*** | |
| Observations | 20 |
| R2 | 0.814 |
| Adjusted R2 | 0.792 |
| Residual Std. Error | 0.685 (df = 17) |
| F Statistic | 37.234*** (df = 2; 17) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (2Q2024 – 3Q2025)
| MAE | 0.344 |
| Last-print MAE | 0.35 |
| RMSE | 0.415 |
| R2 | -1.656 |
Chart forecast uses the OLS fit (beats last-print MAE).
R2 impact
Train ΔR2 is the gain when the term was added. Test ΔR2 is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.
| Variable | Train ΔR2 | Test ΔR2 |
|---|---|---|
| LN_10-year Treasury Yield | +0.6347 | +86.0793 |
| LN_SP500 Stock Price Index | +0.1794 | +12847.3293 |