Forecast a Univariate Series

This guide shows you how to initialize a Chronax model, fit it to a single time series, and generate future predictions. Use this approach when you have a single target variable without external influences.

Prerequisites

Chronax installed (pip install chronax).
The input time series y must be a 1-D jnp.ndarray of type float32.

import jax.numpy as jnp
from chronax.models import AutoARIMA # Assuming AutoARIMA is available

Steps

1. Prepare the input data

Define your historical time series data y. Chronax models expect JAX arrays (jnp.ndarray).

# Example: 20 historical observations
y = jnp.array([
    10.1, 10.5, 11.2, 10.9, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0,
    14.5, 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0
], dtype=jnp.float32)

2. Initialize the model

Instantiate the desired forecasting model. We use AutoARIMA as an example, which automatically selects the best ARIMA parameters.

# NOTE: The specific constructor arguments are missing from the provided specification.
# We assume a default initialization is possible.
model = AutoARIMA() # TODO: confirm AutoARIMA constructor arguments against the API

3. Fit the model to the data

Call the fit method, passing the historical time series y. The model learns the underlying patterns, trend, and seasonality from this data.

params = model.fit(y)

4. Generate the forecast

Use the predict method on the fitted parameters to generate future values. You must specify the forecast horizon h. Here, we forecast 5 steps ahead.

h = 5
forecast_out = model.predict(params, h=h)

# Access the mean forecast values
mean_forecast = forecast_out["mean"]

print(f"Forecasted values for the next {h} steps:")
print(mean_forecast)

Full example

This block combines all steps to initialize, fit, and forecast a univariate series.

import jax.numpy as jnp
from chronax.models import AutoARIMA

# 1. Prepare data
y = jnp.array([
    10.1, 10.5, 11.2, 10.9, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0,
    14.5, 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0
], dtype=jnp.float32)

# 2. Initialize model
model = AutoARIMA() # TODO: confirm AutoARIMA constructor arguments against the API

# 3. Fit the model
params = model.fit(y)

# 4. Generate the forecast (5 steps ahead)
h = 5
forecast_out = model.predict(params, h=h)

# Extract the results
mean_forecast = forecast_out["mean"]

print(f"Historical data length: {len(y)}")
print(f"Forecast horizon (h): {h}")
print(f"Mean forecast: {mean_forecast}")

Next steps

See the guide on "Adding prediction intervals" using the level argument in model.predict.
Explore other models like HoltWinters for series with clear trend and seasonality.
Learn how to use the convenience function model.forecast for combined fit and predict operations.