Initial commit

skills/aeon/references/forecasting.md

@@ -0,0 +1,140 @@
+# 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
+
+```python
+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:
+
+```python
+# 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:
+
+```python
+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:
+
+```python
+# 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.