ARIMA

Forecasting time series

1. ARIMA and SARIMA are both statistical models used for forecasting time series data, where the goal is to predict future points in the series.

2. Business Uses: I got my start with ARIMA using it to predict sales demand (demand forecasting). But ARIMA and forecasting are also used heavily in econometrics, finance, retail, energy demand, and any situation where you need to know the future based on historical time series data.

3. ARIMA Decomposed: AR-I-MA stands for Autoregressive (AR), Integrated (I), Moving Average (MA).

4. Autoregressive (AR): This part of the model captures the relationship between an observation and a specified number of lagged observations.

5. Integrated (I): This involves differencing the time series data to make it stationary. A stationary time series is one whose properties do not depend on the time at which the series is observed, meaning it doesn't have trends or seasonal patterns.

6. Moving Average (MA): This part of the model allows the modeling of the error term as a linear combination of error terms occurring contemporaneously and at various times in the past.

7. Lowercase pdq notation: A non-seasonal ARIMA model is denoted as ARIMA(p, d, q) where: p is the number of lag observations in the model (AR part). d is the degree of differencing required to make the time series stationary. q is the size of the moving average window (MA part).

8. Linear Regression: The ARIMA is simply a Linear Regression model that includes the autoregressive (AR) components and the “moving average” (MA) aka the error terms.

9. SARIMA: Seasonal Autoregressive Integrated Moving-Average extends ARIMA by supporting Seasonal component(s).

10. PDQ-M Notation: Uppercase PDQ defines the orders, which are multiplied by M, the seasonal period (e.g. 4 for quarterly or 12 for monthly).