ARIMA & SARIMA Models in AI & Artificial Intelligence

An ARIMA model is defined by three parameters: p (AutoRegressive), d (Integrated), and q (Moving Average). The 'p' represents how many past values the model looks at to predict the next one. The 'd' represents how many times the data was differenced to remove trends and achieve 'Stationarity'. The 'q' represents the size of the moving average window applied to past forecast errors. By tuning these three numbers, you can model a vast range of time series behaviors, from stock prices to website traffic.

Standard ARIMA fails when data has a repeating cycle, such as higher retail sales every weekend or increased energy consumption every summer. SARIMA (Seasonal ARIMA) solves this by adding a second set of (P, D, Q) parameters specifically for the seasonal period s. For example, in monthly data, s=12. The model then looks at the correlation between the current month and the same month in previous years, allowing it to accurately forecast recurring spikes and dips that a standard model would miss.

While simple moving averages are great, they don't handle complex trends. In this lesson, we'll master ARIMA and SARIMA—the workhorses of statistical time series forecasting.

ARIMA stands for AutoRegressive Integrated Moving Average. It combines 'AR' (past values), 'I' (differencing to make data stationary), and 'MA' (past errors).

For data with seasonal patterns (like sales spikes every December), we use SARIMA. The 'S' stands for Seasonal, adding seasonal parameters to the ARIMA model.

Checkpoint: What does the 'Integrated' (I) part of ARIMA specifically do to the data?

• →It makes it colorful
• →It uses differencing to remove trends and make the data stationary (mean and variance constant over time)

We use the ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) plots to find the optimal values for p and q. This is the 'Identification' phase.

SARIMA allows us to model complex cycles. If you have weekly data with a 52-week cycle, SARIMA can learn to predict the same spike every year with high precision.

Checkpoint: When should you choose SARIMA over a standard ARIMA model?

• →When you want a faster model
• →When your data exhibits clear, repeating seasonal patterns (like daily, weekly, or yearly cycles)

By mastering these statistical models, you build a solid foundation for forecasting before moving into deep learning approaches like LSTMs.

Pro-tip: Use the AIC (Akaike Information Criterion) to compare models. A lower AIC indicates a better balance between model fit and complexity (preventing overfitting).

Checkpoint: True or False: Differencing (d=1) is the process of subtracting the previous value from the current value.

• →True
• →False

Forecasting engine calibrated! Your statistical predictions are now statistically sound.

Next, we'll dive into Feature Engineering for Time Series, learning how to create lag features and rolling windows.

Difference a Real Series. Finish differencing the series — the 'I' (Integrated) step in ARIMA that removes trend.