Editing Openai/693eaf5a-1494-8007-b1e3-00abefb11523 (section)

=== 1. Loss: choose MSE, MAE or MAPE. For price-level fitting MSE or MAE is fine; for relative error MAPE is meaningful. Example: ===

loss=1N∑i=1N(p^i−pi)2\text{loss} = \frac{1}{N}\sum_{i=1}^N (\hat p_{i} - p_{i})^2loss=N1i=1∑N(p^i−pi)2
# Train / Validation split: use walk-forward (rolling) validation rather than a single random split: - Choose a training window length (e.g., 180 days), step forward by 1 day: fit parameters on training window, predict next day, store error; then slide the window forward. This simulates real-time deployment and avoids look-ahead bias.
# Optimization: - For small parameter sets use grid search for robustness. - For continuous parameter spaces use scipy.optimize.minimize (L-BFGS-B) with bounds, or use gradient-free methods (Nelder-Mead) if non-smooth. - Penalize complexity with L2 regularization on parameters.
# Regularization & constraints: - Constrain α,β,k\alpha, \beta, kα,β,k to reasonable ranges (e.g., [-5, 5] or [0, 10]) to avoid blowups. - Add regularization term to loss: lossreg=loss+λ∑θ2\text{loss}_{\text{reg}} = \text{loss} + \lambda \sum \theta^2lossreg=loss+λ∑θ2
# Baseline comparisons: - Always compare to naive baselines: last-price (p_t), simple moving average forecast, and an AR(1) model. If tetrahedral model doesn’t beat these, it likely overfits or is mis-specified.