Time Series Forecasting

Aeon provides forecasting algorithms for predicting future time series values.

Naive and Baseline Methods

Simple forecasting strategies for comparison:

• NaiveForecaster - Multiple strategies: last value, mean, seasonal naive
  • Parameters: strategy ("last", "mean", "seasonal"), sp (seasonal period)
  • Use when: Establishing baselines or simple patterns

Statistical Models

Classical time series forecasting methods:

ARIMA

• ARIMA - AutoRegressive Integrated Moving Average
  • Parameters: p (AR order), d (differencing), q (MA order)
  • Use when: Linear patterns, stationary or difference-stationary series

Exponential Smoothing

• ETS - Error-Trend-Seasonal decomposition
  • Parameters: error, trend, seasonal types
  • Use when: Trend and seasonal patterns present

Threshold Autoregressive

• TAR - Threshold Autoregressive model for regime switching
• AutoTAR - Automated threshold discovery
  • Use when: Series exhibits different behaviors in different regimes

Theta Method

• Theta - Classical Theta forecasting
  • Parameters: theta, weights for decomposition
  • Use when: Simple but effective baseline needed

Time-Varying Parameter

• TVP - Time-varying parameter model with Kalman filtering
  • Use when: Parameters change over time

Deep Learning Forecasters

Neural networks for complex temporal patterns:

• TCNForecaster - Temporal Convolutional Network

  • Dilated convolutions for large receptive fields
  • Use when: Long sequences, need non-recurrent architecture

• DeepARNetwork - Probabilistic forecasting with RNNs

  • Provides prediction intervals
  • Use when: Need probabilistic forecasts, uncertainty quantification

Regression-Based Forecasting

Apply regression to lagged features:

• RegressionForecaster - Wraps regressors for forecasting
  • Parameters: window_length, horizon
  • Use when: Want to use any regressor as forecaster

Quick Start

from aeon.forecasting.naive import NaiveForecaster
from aeon.forecasting.arima import ARIMA
import numpy as np

# Create time series
y = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

# Naive baseline
naive = NaiveForecaster(strategy="last")
naive.fit(y)
forecast_naive = naive.predict(fh=[1, 2, 3])

# ARIMA model
arima = ARIMA(order=(1, 1, 1))
arima.fit(y)
forecast_arima = arima.predict(fh=[1, 2, 3])

Forecasting Horizon

The forecasting horizon (fh) specifies which future time points to predict:

# Relative horizon (next 3 steps)
fh = [1, 2, 3]

# Absolute horizon (specific time indices)
from aeon.forecasting.base import ForecastingHorizon
fh = ForecastingHorizon([11, 12, 13], is_relative=False)

Model Selection

• Baseline: NaiveForecaster with seasonal strategy
• Linear patterns: ARIMA
• Trend + seasonality: ETS
• Regime changes: TAR, AutoTAR
• Complex patterns: TCNForecaster
• Probabilistic: DeepARNetwork
• Long sequences: TCNForecaster
• Short sequences: ARIMA, ETS

Evaluation Metrics

Use standard forecasting metrics:

from aeon.performance_metrics.forecasting import (
    mean_absolute_error,
    mean_squared_error,
    mean_absolute_percentage_error
)

# Calculate error
mae = mean_absolute_error(y_true, y_pred)
mse = mean_squared_error(y_true, y_pred)
mape = mean_absolute_percentage_error(y_true, y_pred)

Exogenous Variables

Many forecasters support exogenous features:

# Train with exogenous variables
forecaster.fit(y, X=X_train)

# Predict requires future exogenous values
y_pred = forecaster.predict(fh=[1, 2, 3], X=X_test)

Base Classes

• BaseForecaster - Abstract base for all forecasters
• BaseDeepForecaster - Base for deep learning forecasters

Extend these to implement custom forecasting algorithms.