Time Series & State Space

NextStat provides a linear-Gaussian Kalman filter with EM parameter estimation, multi-step forecasting, and standard model builders — all computed in Rust.

Kalman Filter

import nextstat.timeseries as ts

# Filter + smooth
filtered = ts.kalman_filter(y, F, H, Q, R, x0, P0)
smoothed = ts.kalman_smooth(y, F, H, Q, R, x0, P0)

# EM parameter estimation
params = ts.kalman_em(y, F, H, n_iter=100)

# Combined fit (filter + EM + smooth)
result = ts.kalman_fit(y, model="local_level")

Forecasting

# Multi-step-ahead with prediction intervals
forecast = ts.kalman_forecast(result, steps=12)

print(forecast.mean)        # point forecasts
print(forecast.lower_95)    # lower 95% PI
print(forecast.upper_95)    # upper 95% PI

Model Builders

• local_level — random walk + noise (structural time series baseline)
• local_trend — random walk with drift
• AR(1) — autoregressive with softplus + bounds transform

Simulation

# Simulate from a fitted model
sim = ts.kalman_simulate(result, n_steps=200, seed=42)

Visualization

from nextstat.timeseries import plot_kalman_states, plot_forecast_bands

plot_kalman_states(smoothed)
plot_forecast_bands(forecast)

Features

• Missing observation handling (skip update, correct likelihood)
• Rauch-Tung-Striebel (RTS) smoother
• EM estimation for Q, R (optionally F, H)
• Controllable seed for reproducible simulation