Forecast a univariate series using AutoARIMA

This guide shows you how to initialize, fit, and forecast a single time series using the AutoARIMA model, which automatically selects the best ARIMA parameters for your data.

Prerequisites

Chronax installed (pip install chronax).
Data must be a 1-D array of observations (y).
y is a jnp.ndarray of type float32.

Steps

1. Prepare the data and import the model

Start by importing the necessary libraries and creating a sample univariate time series (y).

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

# Create a sample time series (e.g., 100 observations)
y = jnp.arange(100, dtype=jnp.float32) + jnp.sin(jnp.linspace(0, 10, 100))

# Define the forecast horizon
H = 10

2. Initialize the AutoARIMA model

Initialize the AutoARIMA model. Since this model automatically handles parameter selection, typically no arguments are required during initialization, but you may specify constraints if needed.

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

3. Fit the model to the historical data

Fit the model using the historical observations (y). The fit method trains the model parameters based on the input data.

# The standard Chronax fit contract is model.fit(y, X=None)
params = model.fit(y)

4. Generate the forecast

Use the predict method on the fitted model to generate forecasts for the desired horizon (H). The output is a dictionary containing the forecast mean and potentially other metrics.

# The standard Chronax predict contract is model.predict(h, level=None)
forecast_output = model.predict(H)

# Access the mean forecast
mean_forecast = forecast_output["mean"]

print(f"Forecast shape: {mean_forecast.shape}")

Full example

This complete example combines the steps to initialize, fit, and forecast a series using AutoARIMA.

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

# 1. Prepare data
y = jnp.arange(100, dtype=jnp.float32) + jnp.sin(jnp.linspace(0, 10, 100))
H = 10

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

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

# 4. Generate the forecast
forecast_output = model.predict(H)

# Access the mean forecast
mean_forecast = forecast_output["mean"]

print(f"Historical data length: {len(y)}")
print(f"Forecast horizon (H): {H}")
print(f"Mean forecast (first 5 points): {mean_forecast[:5]}")

Next steps

See the guide on "Adding prediction intervals" using the level argument in model.predict.
Explore other classical models like SeasonalNaive or Theta.
Learn how to use BatchedForecaster to handle multiple time series efficiently.
Investigate foundation models like chronos or timesfm for complex forecasting tasks.