1. Why Linear Models Still Matter in 2025

In a world obsessed with transformers and "foundation models," linear and regularized regressions still do a lot of quiet, serious work in finance:

• They are fast: you can run a full equity universe in seconds.
• They are interpretable: coefficients look like a factor exposure sheet.
• They provide a clean benchmark for more complex models.

On volarixs, the linear family is our default comparison layer: every fancy model needs to beat a well-regularized linear baseline on out-of-sample Sharpe and drawdown before we get excited.

2. The Core Ideas: From OLS to Elastic Net

We use four core variants:

• OLS / Linear Regression: minimize squared error, no regularization.
• Ridge (L2): penalize large coefficients, shrink them towards zero.
• Lasso (L1): penalize absolute values, force many coefficients to zero (feature selection).
• Elastic Net: combination of L1 and L2; more stable than pure Lasso in correlated features.

The objective functions:

3. Application to Financial Time Series

Key points:

• We transform price data into cross-sectional features at each date (returns, realized vol, rolling betas, etc.).
• We run cross-sectional regressions (all tickers at a given date) or time-series regressions (one asset over time) depending on the setup.
• Regularization helps with:
  • • Noisy factors
  • • High collinearity (value vs quality vs carry, etc.)
  • • High-dimensional feature sets (text, macro, technicals)

4. How volarixs Uses This Family

In volarixs:

• Linear models are used as baseline in experiment mode and as cheap workhorses in the prediction factory.
• We store:
  • • Coefficient vectors per run
  • • Metrics (MSE, MAE, R², Sharpe, max drawdown, hit ratio)
  • • Regime-conditioned performance (e.g. bull vs bear, high vs low vol regimes)