Software Project Reproducible empirical comparison
A Reproducible Comparison of Trend Estimation Methods on S&P 500 Log Prices
Summary
Empirical comparison of train-validation smoothness selection for penalized trends (\widehat{t}(\lambda)) against time-weighted validation and benchmark methods on S&P 500 log prices. The design uses a strict temporal train/validation/test protocol and separates Guerrero smoothness from realized roughness diagnostics.
$$ \widehat{t}(\lambda)=\left(I_N+\lambda K^{\mathsf{T}}K\right)^{-1}z,\qquad S_d(\lambda;N)=1-\frac{\operatorname{tr}S(\lambda)}{N} $$
Context
Hyperparameters are chosen only on past validation windows and evaluated on a held-out temporal test segment.
Main contributions
- Compared train-validation and time-weighted selectors against HP, Whittaker, moving-average, exponential-smoothing, and polynomial baselines.
- Used spectral linear algebra and cached eigendecompositions for efficient penalized trend fitting.
- Mapped Guerrero smoothness to λ through the trace of the smoothing matrix.
- Reported forecast errors, validation curves, local minima, test forecasts, and realized roughness diagnostics.