ARIMA Model

ARIMA stands for AutoRegressive Integrated Moving Average. It is a popular statistical method for time series forecasting.

Simple Explanation

Think of ARIMA as a weather forecaster that looks at patterns of pressure, temperature, and wind speed (past values) to predict the weather (future values). In time series language, ARIMA considers past values (auto-regressive part), trends and seasonality (integrated part), and random shocks (moving average part) to forecast future data points.

Formula

The ARIMA model is represented by three terms: AR(p), I(d), and MA(q), where:

• AR(p) is the auto-regressive part with p indicating the number of lag observations included in the model.
• I(d) is the integrated part, where d is the order of differencing required to make the time series stationary.
• MA(q) is the moving average part with q indicating the size of the moving average window.

The ARIMA model can be formulated as:

(1 - Σ[αₚ * B^p]) (1 - B)^d Yₜ = (1 + Σ[θₑ * B^q]) εₜ

where:

• Yₜ is the time series.
• B is the backshift operator.
• αₚ are the parameters for the AR part.
• θₑ are the parameters for the MA part.
• εₜ is white noise.

Parameters

• p: The number of lag observations in the model.
• d: The degree of differencing.
• q: The size of the moving average window.

Feature Importance

In ARIMA, feature importance isn't discussed in the same way as it is for algorithms like decision trees. Instead, the focus is on the significance of the parameters (αₚ, θₑ) and the lagged values of the time series.

Code

To see how we implemented ARIMA in our project including cross-validation, check out the ARIMA notebook.

Additional Notes

• ARIMA models are fitted to time series data either to better understand the data or to predict future points in the series (forecasting).
• Seasonal ARIMA (SARIMA) is an extension of ARIMA that explicitly supports univariate time series data with a seasonal component.

To learn more about ARIMA and its applications, check out the ARIMA documentation.