30-year Treasury Yield
Linear model of 30-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 labeled by the month after its 12-month test window; the fit uses the prior 48 months of Y. Independents are dated six months earlier than Y.
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 month. 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.
Sept 2026: 30-year Treasury Yield = 8.686 − 4.021 × LN_Unemployment Rate + 6.018e-8 × SP500 Stock Price Index² − 0.076 × CPI Inflation Rate
Train: Sept 2021 – Aug 2025 (48 observations). Test: Sept 2025 – Aug 2026 (11 observations). Independents are dated six months before each Y period.
| Dependent variable (+/- SE): | |
| 30-year Treasury Yield | |
| Constant | 8.686 (+/- 0.347) |
| p = 0.000*** | |
| LN_Unemployment Rate | -4.021 (+/- 0.223) |
| p = 0.000*** | |
| SP500 Stock Price Index2 | 0.00000 (+/- 0.000) |
| p = 0.000*** | |
| CPI Inflation Rate | -0.076 (+/- 0.018) |
| p = 0.0002*** | |
| Observations | 48 |
| R2 | 0.922 |
| Adjusted R2 | 0.917 |
| Residual Std. Error | 0.265 (df = 44) |
| F Statistic | 173.415*** (df = 3; 44) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (Sept 2025 – Aug 2026)
| MAE | 0.262 |
| Last-print MAE | 0.092 |
| RMSE | 0.332 |
| R2 | -5.132 |
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_Unemployment Rate | +0.6354 | +1726.4194 |
| SP500 Stock Price Index² | +0.2549 | +265.4654 |
| CPI Inflation Rate | +0.0317 | -3.6518 |
Aug 2026: 30-year Treasury Yield = 2.236 − 9.550e-4 × Real disposable income growth² + 0.541 × LN_Nominal disposable income growth − 0.492 × LN_CPI Inflation Rate + 3.811e-4 × SP500 Stock Price Index
Train: Aug 2021 – July 2025 (41 observations). Test: Aug 2025 – July 2026 (12 observations). Independents are dated six months before each Y period.
| Dependent variable (+/- SE): | |
| 30-year Treasury Yield | |
| Constant | 2.236 (+/- 0.714) |
| p = 0.004*** | |
| Real disposable income growth2 | -0.001 (+/- 0.0001) |
| p = 0.000*** | |
| LN_Nominal disposable income growth | 0.541 (+/- 0.074) |
| p = 0.000*** | |
| LN_CPI Inflation Rate | -0.492 (+/- 0.131) |
| p = 0.001*** | |
| SP500 Stock Price Index | 0.0004 (+/- 0.0001) |
| p = 0.002*** | |
| Observations | 41 |
| R2 | 0.910 |
| Adjusted R2 | 0.900 |
| Residual Std. Error | 0.266 (df = 36) |
| F Statistic | 90.531*** (df = 4; 36) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (Aug 2025 – July 2026)
| MAE | 0.166 |
| Last-print MAE | 0.088 |
| RMSE | 0.203 |
| R2 | -1.494 |
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 |
|---|---|---|
| Real disposable income growth² | +0.1166 | -0.0113 |
| LN_Nominal disposable income growth | +0.0942 | +39.4575 |
| LN_CPI Inflation Rate | +0.1009 | +10.5429 |
| SP500 Stock Price Index | +0.0348 | +336.1074 |
July 2026: 30-year Treasury Yield = -33.872 − 0.283 × Nominal GDP growth + 3.74 × LN_US Avg Retail Gasoline Price ($-gal; all grades, all formulations) + 0.219 × Real GDP growth + 5.938e-10 × Dow Total Stock Market Index² + 5.752 × LN_Commercial Real Estate Price Index
Train: July 2021 – June 2025 (48 observations). Test: July 2025 – June 2026 (12 observations). Independents are dated six months before each Y period.
| Dependent variable (+/- SE): | |
| 30-year Treasury Yield | |
| Constant | -33.872 (+/- 9.970) |
| p = 0.002*** | |
| Nominal GDP growth | -0.283 (+/- 0.032) |
| p = 0.000*** | |
| LN_US Avg Retail Gasoline Price ($-gal; all grades, all formulations) | 3.740 (+/- 0.870) |
| p = 0.0002*** | |
| Real GDP growth | 0.219 (+/- 0.058) |
| p = 0.001*** | |
| Dow Total Stock Market Index2 | 0.000 (+/- 0.000) |
| p = 0.00005*** | |
| LN_Commercial Real Estate Price Index | 5.752 (+/- 1.824) |
| p = 0.003*** | |
| Observations | 48 |
| R2 | 0.845 |
| Adjusted R2 | 0.827 |
| Residual Std. Error | 0.404 (df = 42) |
| F Statistic | 45.831*** (df = 5; 42) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (July 2025 – June 2026)
| MAE | 0.569 |
| Last-print MAE | 0.078 |
| RMSE | 0.619 |
| R2 | -32.373 |
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 |
|---|---|---|
| Nominal GDP growth | +0.4997 | +62.9741 |
| LN_US Avg Retail Gasoline Price ($-gal; all grades, all formulations) | +0.1474 | +2105.3450 |
| Real GDP growth | +0.1172 | +91.5181 |
| Dow Total Stock Market Index² | +0.0442 | +536.1783 |
| LN_Commercial Real Estate Price Index | +0.0367 | +96977.0099 |
June 2026: 30-year Treasury Yield = -32.648 − 0.284 × Nominal GDP growth + 3.692 × LN_US Avg Retail Gasoline Price ($-gal; all grades, all formulations) + 0.221 × Real GDP growth + 5.327e-10 × Dow Total Stock Market Index² + 5.571 × LN_Commercial Real Estate Price Index
Train: June 2021 – May 2025 (48 observations). Test: June 2025 – May 2026 (12 observations). Independents are dated six months before each Y period.
| Dependent variable (+/- SE): | |
| 30-year Treasury Yield | |
| Constant | -32.648 (+/- 9.992) |
| p = 0.003*** | |
| Nominal GDP growth | -0.284 (+/- 0.031) |
| p = 0.000*** | |
| LN_US Avg Retail Gasoline Price ($-gal; all grades, all formulations) | 3.692 (+/- 0.818) |
| p = 0.0001*** | |
| Real GDP growth | 0.221 (+/- 0.057) |
| p = 0.0004*** | |
| Dow Total Stock Market Index2 | 0.000 (+/- 0.000) |
| p = 0.0004*** | |
| LN_Commercial Real Estate Price Index | 5.571 (+/- 1.827) |
| p = 0.004*** | |
| Observations | 48 |
| R2 | 0.851 |
| Adjusted R2 | 0.833 |
| Residual Std. Error | 0.401 (df = 42) |
| F Statistic | 47.814*** (df = 5; 42) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (June 2025 – May 2026)
| MAE | 0.672 |
| Last-print MAE | 0.073 |
| RMSE | 0.717 |
| R2 | -47.552 |
Chart forecast uses the last-print baseline (OLS MAE is worse).
R2 impact
Train ΔR2 is the gain when the term was added. Test ΔR2 is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.
| Variable | Train ΔR2 | Test ΔR2 |
|---|---|---|
| Nominal GDP growth | +0.4481 | +36.1695 |
| LN_US Avg Retail Gasoline Price ($-gal; all grades, all formulations) | +0.2144 | +2324.3315 |
| Real GDP growth | +0.1293 | +117.5941 |
| Dow Total Stock Market Index² | +0.0256 | +493.0468 |
| LN_Commercial Real Estate Price Index | +0.0331 | +99282.9350 |
May 2026: 30-year Treasury Yield = 5.786 − 0.068 × Unemployment Rate² − 0.933 × LN_CPI Inflation Rate + 0.002 × Real GDP growth² + 0.047 × US Avg Retail Gasoline Price ($-gal; all grades, all formulations)² − 9.160e-5 × Nominal disposable income growth²
Train: May 2021 – Apr 2025 (48 observations). Test: May 2025 – Apr 2026 (12 observations). Independents are dated six months before each Y period.
| Dependent variable (+/- SE): | |
| 30-year Treasury Yield | |
| Constant | 5.786 (+/- 0.259) |
| p = 0.000*** | |
| Unemployment Rate2 | -0.068 (+/- 0.006) |
| p = 0.000*** | |
| LN_CPI Inflation Rate | -0.933 (+/- 0.100) |
| p = 0.000*** | |
| Real GDP growth2 | 0.002 (+/- 0.0003) |
| p = 0.000*** | |
| US Avg Retail Gasoline Price ($-gal; all grades, all formulations)2 | 0.047 (+/- 0.018) |
| p = 0.012** | |
| Nominal disposable income growth2 | -0.0001 (+/- 0.00004) |
| p = 0.035** | |
| Observations | 48 |
| R2 | 0.935 |
| Adjusted R2 | 0.927 |
| Residual Std. Error | 0.266 (df = 42) |
| F Statistic | 120.158*** (df = 5; 42) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (May 2025 – Apr 2026)
| MAE | 0.576 |
| Last-print MAE | 0.078 |
| RMSE | 0.663 |
| R2 | -57.385 |
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 |
|---|---|---|
| Unemployment Rate² | +0.6348 | +4.5860 |
| LN_CPI Inflation Rate | +0.1366 | -44.6487 |
| Real GDP growth² | +0.1460 | +2.6695 |
| US Avg Retail Gasoline Price ($-gal; all grades, all formulations)² | +0.0098 | +106.8080 |
| Nominal disposable income growth² | +0.0074 | -0.3027 |
Apr 2026: 30-year Treasury Yield = 5.797 − 0.067 × Unemployment Rate² + 0.002 × Real GDP growth² − 0.946 × LN_CPI Inflation Rate + 0.048 × US Avg Retail Gasoline Price ($-gal; all grades, all formulations)² − 9.249e-5 × Nominal disposable income growth²
Train: Apr 2021 – Mar 2025 (48 observations). Test: Apr 2025 – Mar 2026 (12 observations). Independents are dated six months before each Y period.
| Dependent variable (+/- SE): | |
| 30-year Treasury Yield | |
| Constant | 5.797 (+/- 0.260) |
| p = 0.000*** | |
| Unemployment Rate2 | -0.067 (+/- 0.006) |
| p = 0.000*** | |
| Real GDP growth2 | 0.002 (+/- 0.0003) |
| p = 0.000*** | |
| LN_CPI Inflation Rate | -0.946 (+/- 0.106) |
| p = 0.000*** | |
| US Avg Retail Gasoline Price ($-gal; all grades, all formulations)2 | 0.048 (+/- 0.018) |
| p = 0.011** | |
| Nominal disposable income growth2 | -0.0001 (+/- 0.00004) |
| p = 0.033** | |
| Observations | 48 |
| R2 | 0.936 |
| Adjusted R2 | 0.928 |
| Residual Std. Error | 0.266 (df = 42) |
| F Statistic | 121.986*** (df = 5; 42) |
| Note: | *p<0.1; **p<0.05; ***p<0.01 |
Test period (Apr 2025 – Mar 2026)
| MAE | 0.502 |
| Last-print MAE | 0.083 |
| RMSE | 0.606 |
| R2 | -47.696 |
Chart forecast uses the last-print baseline (OLS MAE is worse).
R2 impact
Train ΔR2 is the gain when the term was added. Test ΔR2 is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.
| Variable | Train ΔR2 | Test ΔR2 |
|---|---|---|
| Unemployment Rate² | +0.5956 | +32.9588 |
| Real GDP growth² | +0.1925 | +1.6179 |
| LN_CPI Inflation Rate | +0.1302 | -31.5141 |
| US Avg Retail Gasoline Price ($-gal; all grades, all formulations)² | +0.0098 | +97.1343 |
| Nominal disposable income growth² | +0.0075 | -0.2859 |