Forecasting

dynaris produces multi-step-ahead forecasts with uncertainty intervals by iterating the state-space prior equations forward without new observations.

Basic forecasting

After fitting (and optionally smoothing), call forecast:

from dynaris import LocalLinearTrend, Seasonal, DLM
from dynaris.datasets import load_airline

y = load_airline()
model = LocalLinearTrend() + Seasonal(period=12)
dlm = DLM(model)
dlm.fit(y).smooth()

forecast_df = dlm.forecast(steps=24)
print(forecast_df)
#            mean     lower_95    upper_95
# ...

The returned DataFrame contains the forecast mean and 95% confidence bands.

DatetimeIndex propagation

If you fit with a pandas Series that has a DatetimeIndex, the forecast DataFrame continues the date index:

# y has monthly DatetimeIndex 1949-01 to 1960-12
forecast_df = dlm.forecast(steps=12)
# Index continues: 1961-01, 1961-02, ...

Filtered vs smoothed initialization

Forecasts can start from either the filtered or smoothed terminal state:

• Filtered (default after fit): uses only past observations up to time \(T\)

• Smoothed (after smooth): uses the full dataset, giving a more refined starting point

The lower-level functions give explicit control:

from dynaris.forecast import forecast_from_filter, forecast_from_smoother

fc_filt = forecast_from_filter(filter_result, model, steps=12)
fc_smooth = forecast_from_smoother(smoother_result, model, steps=12)

Confidence bands

Confidence bands widen with the forecast horizon as evolution noise accumulates:

from dynaris.forecast import confidence_bands

lower, upper = confidence_bands(forecast_result, level=0.95)

Visualize with:

dlm.plot(kind="forecast", n_history=36)

See Forecasting for the full API.