generator_v2 — SARIMA-compositional + chaotic + long-memory cascade generator

What's inside

Core families (selected per series by core_weights)

1. SARIMA-compositional (dominant, best single scorer) — regime-switching SARIMA(p,d,q)(P,D,Q)_s with stochastic volatility, fat tails, integration.
2. Chaotic dynamical systems (new) — continuous chaotic flows integrated by RK4 (Lorenz, Rössler, Thomas, Chen, driven Van der Pol) plus the Mackey-Glass delay system. Motivated by DynaMix (NeurIPS'25): a TSFM trained purely on a small library of chaotic attractors generalises zero-shot to real traffic/weather. These give deterministic-but-complex, broadband, long-range structure no ARMA prior contains.
3. Long-memory / fractional (new) — (i) power-law 1/f^β colored-noise spectral synthesis (β∈[-1,3]: anti-persistent → pink → Brownian), and (ii) ARFIMA(p,d,0) via truncated fractional-differencing (Hosking) coefficients. Fills the gap between SARIMA's I(0) and I(1) with genuine long-range dependence (Hurst ≠ 0.5).
4. Bilinear nonlinear-AR (new) — y_t = φ y_{t-1} + b y_{t-1} e_{t-1} + θ e_{t-1} + e_t: bursty multiplicative autocorrelation distinct from SETAR/GARCH.

Performance & stability

• The chaotic cores use a bounded scalar recursion capped at chaos_max_steps (default 1200) integration steps and then resample to the target length, so cost stays linear and small even at length 4096.
• Any core that diverges or returns non-finite falls back deterministically to the SARIMA core; the final series is rescaled and hard-clipped to max_abs_value.
• SARIMA AR/MA roots are guaranteed outside the unit circle (Levinson-Durbin on reflection coefficients); ARFIMA uses d < 0.5 for stationarity.

Determinism

Verify

Config knobs (config.json)

• min_length / max_length — per-series length band.
• core_weights — probability mass over sarima / chaotic / longmem / bilinear cores. SARIMA is kept dominant (strongest single scorer).
• chaos_min_steps / chaos_max_steps — chaotic integration-step budget (bounds cost; trajectories are resampled to the series length).
• max_ar / max_ma / max_seasonal_ar / max_seasonal_ma — SARIMA caps.
• d_weights / seasonal_d_weights — integration-order probability mass.
• seasonal_prob / student_t_prob / stoch_vol_prob — SARIMA innovations.
• regime_prob / max_regimes — regime-switching frequency and count.
• trend_prob / calendar_prob / level_shift_prob / spike_prob — components.
• warp_prob / mixup_prob — nonlinear marginal warp / TSMixup probabilities.
• standardize — z-normalise each series (default false).
• max_abs_value — hard magnitude clip to keep output trainer-safe finite.