Demonstrates time-series forecasting using the N-BEATS (Neural Basis Expansion Analysis for Interpretable Time Series Forecasting) model from the timeseries package.

1. Model configuration -- setting up N-BEATS with trend and seasonality stacks
2. Synthetic data generation -- creating a time series with trend + seasonal pattern
3. Forward pass -- running inference to produce a multi-step forecast
4. Interpretable decomposition -- examining per-stack (trend, seasonality) forecast components

go build -o ts-forecast ./examples/timeseries/

./ts-forecast

=== N-BEATS Time-Series Forecasting Example ===

Model configuration:
  Input length:      24
  Output length:     6
  Stacks:            trend + seasonality
  Blocks per stack:  2
  Hidden dim:        32
  Fourier harmonics: 4

N-BEATS model created successfully.

Generating synthetic data: batch_size=2, seq_len=24
Input (first batch element):
  [0.0000, 5.5000, 9.1603, ...]

--- Forecast (horizon=6) ---
Batch 0 forecast:
  [x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx]
Batch 1 forecast:
  [x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx]

--- Stack Decomposition ---
trend stack (batch 0):
  [x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx]
seasonality stack (batch 0):
  [x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx, x.xxxx]

=== Done ===

The actual forecast values depend on the randomly initialized model weights. With training on real data, N-BEATS learns to decompose the signal into meaningful trend and seasonality components.

N-BEATS uses a stack of blocks with double residual connections:

1. Each block applies FC layers to produce theta parameters
2. Theta is expanded through a basis function:
   • Trend: polynomial basis (captures linear/quadratic trends)
   • Seasonality: Fourier basis (captures periodic patterns)
   • Generic: learned linear projections
3. The backcast is subtracted from the input (residual connection)
4. The forecast is accumulated across all blocks

This architecture provides interpretable decomposition -- you can inspect what each stack contributes to the final forecast.

• PatchTST: Patch Time-Series Transformer for channel-independent forecasting. Use timeseries.NewPatchTST(config, engine, ops).
• TFT: Temporal Fusion Transformer with attention-based interpretability.