What is SARIMA, and how is it different from ARIMA?

SARIMA (Seasonal AutoRegressive Integrated Moving Average) is a time series forecasting model that extends ARIMA (AutoRegressive Integrated Moving Average) by incorporating seasonal patterns. ARIMA models are designed to capture trends and dependencies in non-seasonal data using three parameters: p (autoregressive order), d (differencing order), and q (moving average order). SARIMA adds four seasonal parameters: P (seasonal autoregressive), D (seasonal differencing), Q (seasonal moving average), and m (seasonal period length, e.g., 12 for monthly data with yearly seasonality). This allows SARIMA to model both non-seasonal and recurring seasonal effects, making it more flexible for datasets with periodic patterns.

The key difference lies in how SARIMA handles seasonality. For example, ARIMA might model a monthly sales trend but fail to account for a yearly holiday spike. SARIMA addresses this by adding seasonal terms that explicitly model repeating patterns. A SARIMA model is denoted as SARIMA(p, d, q)(P, D, Q)m. The first set of parentheses represents the non-seasonal ARIMA components, while the second set defines the seasonal adjustments. For instance, if monthly sales data shows a yearly pattern (m=12), SARIMA could use P=1 to capture the autoregressive effect of the previous year’s December sales on the current December. Differencing (D) might remove a seasonal trend, like subtracting the previous year’s value from each data point.

A practical example helps illustrate this. Suppose you’re forecasting electricity demand, which spikes daily (e.g., higher usage at 6 PM) and seasonally (e.g., higher usage in winter). ARIMA could model the overall trend and daily fluctuations but might miss the yearly winter surge. SARIMA, with m=365 (daily data) or m=12 (monthly data), would model both daily and yearly patterns. Implementing SARIMA in Python with statsmodels requires specifying the seasonal parameters alongside the standard ARIMA terms, whereas ARIMA would ignore them. This makes SARIMA more complex but necessary for datasets where seasonality is a critical factor.