ARIMA

ARIMA (AutoRegressive Integrated Moving Average) is a popular method for Time Series Forecasting that models the autocorrelations within the data. It is particularly useful for datasets with trends and patterns that are not seasonal. However, it is not perfect; for example, it struggles with predicting stock trading data.

ARIMA Explained

ARIMA stands for:

• AutoRegressive (AR): Uses past values to predict the current one.
• Integrated (I): Differencing to make the series stationary.
• MAving Average (MA): Uses past forecast errors for prediction.

A typical ARIMA(p,d,q) model has:

• $p$: Number of lagged values (AR terms)
• $d$: Number of differences needed to make the series stationary
• $q$: Number of lagged forecast errors (MA terms)

What ARIMA Does:

1. Checks for stationarity – if not, applies differencing ($d$ times).
2. Models relationships between current values and:
   • Past values (AR part)
   • Past errors (MA part)
3. Fits parameters by minimizing a loss (typically log-likelihood).
4. Forecasts future values using this learned structure.

Why ARIMA Isn’t Enough for Seasonal Data

Data might show repeating patterns every 4 quarters (seasonality), and ARIMA has no built-in mechanism to model this periodic structure. This is where SARIMA comes in.

Summary

Model	Handles Trend	Handles Seasonality	Use When…
ARIMA	✅	❌	Data has trend, but no regular cycles
SARIMA	✅	✅	Data has both trend and seasonality

Related terms

In ML_Tools see:

• https://github.com/rhyslwells/ML_Tools/blob/main/Explorations/Build/TimeSeries/ARIMA.ipynb
• Forecasting_AutoArima.py
• pmdarima