Examples

Ready-to-run scripts demonstrating dynaris on real-world datasets. Each example lives in the examples/ directory of the repository.

Classic / Introductory

Nile River Flow — nile_river.py

Local level model on annual Nile discharge (1871–1970). The simplest possible DLM: a random walk observed with noise. Demonstrates fitting, smoothing, and forecasting.

Trend + Seasonality — trend_seasonal.py

Simulated sales data with a local linear trend and monthly seasonality. Shows how to compose components and extract individual contributions.

Economics & Finance

Airline Passengers — airline_passengers.py

Box-Jenkins airline data (1949–1960). Trend plus seasonal decomposition, forecasting, and component visualization.

GDP Business Cycle — gdp_business_cycle.py

US quarterly GDP growth. Local level plus AR(2) to capture business cycle dynamics.

Stochastic Volatility — stochastic_volatility.py

Particle filter on a stochastic volatility model for financial returns. Compares EKF, UKF, and particle filter on latent log-volatility recovery using the Kim-Shephard-Chib linearization.

Regime Switching — regime_switching.py

Hamilton filter and Kim smoother detecting volatility regimes. Simulates a 2-regime process (calm vs volatile) and tracks filtered and smoothed regime probabilities over time.

Natural Sciences

Lynx Population — lynx_population.py

Canadian lynx trappings (1821–1934). Uses an autoregressive component to model the ~10-year population cycle.

Sunspot Cycles — sunspot_cycles.py

Annual sunspot numbers (1700–1987). Level plus cycle component to detect the ~11-year solar cycle.

Global Temperature — global_temperature.py

Annual temperature anomaly (1880–2023). Linear trend detection in climate data.

Nonlinear Filtering

Lorenz Attractor Tracking — lorenz_tracking.py

Compares EKF, UKF, and particle filter on the chaotic Lorenz system. Simulates a 3D trajectory with partial (2D) noisy observations and tracks the full state. Plots per-component tracking accuracy.

Bearings-Only Tracking — bearings_tracking.py

EKF on a 2D target tracking problem with nonlinear bearing-angle observations. Demonstrates the classic radar/sonar tracking scenario where the sensor measures only the angle to the target.

Bayesian Estimation

Bayesian Airline Passengers — bayesian_nile.py

Full Bayesian inference for a trend + seasonal model on log-transformed airline data using NumPyro’s NUTS sampler. Compares posterior with MLE, generates posterior predictive forecasts with credible intervals, and runs prior predictive checks.

Dynamic Factor Models

Macroeconomic Nowcasting — macro_nowcasting.py

Extracts 2 latent factors from a panel of 10 simulated macroeconomic indicators via DFM-EM. Plots factor time series, loading matrix heatmap, explained variance, and multivariate forecasts.

Multi-Sensor Fusion — sensor_fusion.py

Fuses 5 noisy temperature sensors into a single optimal estimate using a 1-factor DFM. Demonstrates how the DFM weights sensors by their reliability (inverse noise variance).

Advanced

Dynamic Regression — dynamic_regression.py

Time-varying regression coefficients. Shows how regression weights evolve over time when sigma_reg > 0.

Panel Overview — panel_overview.py

Demonstrates the multi-panel plot combining filtered, smoothed, forecast, and diagnostic views in a single figure.