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MARGenerator draws mixture autoregressive (MAR) series for foundation-model pretraining. At each time step it selects an autoregressive component and uses that component’s intercept, lag coefficients, and innovation scale: yt=ck+∑i=1pkϕk,iyt−i+σkεt.y_t = c_k + \sum_{i=1}^{p_k} \phi_{k,i} y_{t-i} + \sigma_k \varepsilon_t. The mixture autoregressive model is due to Wong and Li (2000); the breadth-oriented sampling recipe follows GRATIS. SynForecast samples stationary coefficients through partial autocorrelations and adds bounded retries, optional seasonal AR factors, and explicit output standardization.

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Generate a diverse MAR pool

Random mode samples a new configuration for every series. seasonal_period enables a seasonal AR factor for a random subset of components.
Bulk generate() calls use the native Rust batch path and are deterministic for a fixed seed regardless of worker count. The native and Python reference paths implement the same model contract but use different RNG streams, so do not compare generate() output bit-for-bit with successive generate_single_series() calls. By default each accepted series is standardized to population mean zero and standard deviation one. Set standardize=False when component-implied levels and scales are part of the desired distribution.

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Supply a fixed MAR model

Fixed mode is enabled by supplying all four fixed fields together. Every AR component must be stationary and the mixture must be second-order stationary (Wong and Li 2000); weights are normalized during validation. seasonal_period has no effect in fixed mode. A fixed model whose simulation fails the finite, bounded, non-constant output guards raises a ValueError instead of silently returning noise.
weights, ar_coefficients, intercepts, and noise_scales are an all-or-nothing group. Leaving all four unset selects random mode.

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Target time-series features

tune_to_features searches for one fixed MAR configuration whose realized features approach a target. Supported features are spectral_entropy, trend_strength, seasonal_strength, and acf1.
Candidate fitness is averaged over deterministic lengths spanning the requested range, and feature computation runs in Rust. Targets describe a distribution, not an exact per-series constraint: evaluate the realized feature distribution at the lengths and seeds used downstream. Seasonal-strength targeting also requires seasonal_period and at least two complete periods at min_length.
Note The search evaluates at most the product of n_generations, population_size, and n_draws_per_candidate simulated paths, stopping early once the best L2 feature distance is at or below tolerance (default 0.05). Infeasible targets return the best candidate found within that fixed budget. tuning_diagnostics reports best_distance, converged, generations_run, and candidates_evaluated. The distance is the selected candidate’s observed search fitness; evaluate fresh draws to measure performance on new samples.

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When to use MAR

Use MAR when you want many stationary or seasonally autoregressive shapes from a compact model family, or when a pretraining corpus needs controlled coverage of autocorrelation and entropy. For decomposed trend/seasonal/irregular compositions use TSI; for random causal graphs and nonlinear lead-lag structure use TCM; for Gaussian-process kernel compositions use KernelSynth. Full constructor parameters are listed in the generator reference.