Components of ARIMA: ARIMA is an acronym for AutoRegressive Integrated Moving Average. It consists of three main components: AutoRegressive (AR), Integrated (I), and Moving Average (MA). The AR component represents the autoregressive part, the I component represents differencing to make the time series stationary, and the MA component represents the moving average part.
Stationarity Requirement: ARIMA models assume that the time series is stationary, meaning that its statistical properties (such as mean and variance) do not change over time. If the time series is not stationary, differencing is applied to make it stationary before fitting the ARIMA model.
ARIMA(p, d, q): The notation ARIMA(p, d, q) represents the order of the ARIMA model, where “p” is the order of the autoregressive part, “d” is the degree of differencing, and “q” is the order of the moving average part. For example, ARIMA(1, 1, 1) indicates a model with an autoregressive order of 1, a differencing of order 1, and a moving average order of 1.
Seasonal ARIMA (SARIMA): SARIMA is an extension of ARIMA that incorporates seasonality. It includes additional seasonal terms (P, D, Q) to account for periodic patterns in the time series. The notation for SARIMA is SARIMA(p, d, q)(P, D, Q)s, where “s” represents the seasonal period.
Model Selection: Choosing the appropriate values for the ARIMA parameters (p, d, q) can be done through model selection techniques such as grid search, where different combinations of parameters are evaluated based on their performance in terms of model fit and prediction accuracy. Additionally, diagnostic tools like ACF (AutoCorrelation Function) and PACF (Partial AutoCorrelation Function) plots are often used to identify the order of the ARIMA model.