Add support for t-distributed innovations in SARIXModel

[nickreich]

Summary

Extends SARIXModel to support t-distributed innovations, enabling more robust forecasting with heavier-tailed error distributions.

Changes

• Extended _get_extra_sarix_params(): Base class now passes through innovation_dist and innovation_df_prior_scale parameters if specified in model_config
• Updated SARIXFourierModel: Properly merges base parameters with Fourier-specific parameters using super()
• Added test_sarix_tdist_innovations(): Integration test validating model runs with t-distributed errors

Dependencies

Requires sarix library with t-distribution support (PR: elray1/sarix#17)

Usage Example

model_config = SimpleNamespace(
    p=6,
    theta_pooling='shared',
    sigma_pooling='none',
    innovation_dist='t',  # Use t-distribution
    innovation_df_prior_scale=10.0,  # Prior mean df = 20
    x=[]
)
model = SARIXModel(model_config)

Testing

• ✅ Integration test passes with t-distributed innovations
• ✅ Model successfully estimates degrees of freedom for each location
• ✅ Forecasts generated correctly with t-distribution
• ✅ Backward compatible (default behavior unchanged)

🤖 Generated with Claude Code

[nickreich]

This is an expected failure until sarix PR is merged. reichlab/sarix#8