What is the ARIMA model and what do its parameters (p, d, q) mean?

ARIMA (AutoRegressive Integrated Moving Average) is a model for analyzing and forecasting time series data, which combines three components:

• AR (p) — autoregression: the model uses the dependence of the current value on the previous p values.
• I (d) — integration: the number of times the original series is differenced to achieve stationarity (removing trend).
• MA (q) — moving average: the model accounts for the influence of the previous q forecast errors.

Parameters:

• p — order of autoregression (number of lags in the AR model).
• d — degree of differencing (how many times the differencing operation is applied to stabilize the series).
• q — order of the moving average (number of lagged errors in the MA model).

Example: ARIMA(2,1,1) means that the series was differenced once, and the model considers 2 previous values and 1 previous forecast error.

ARIMA is widely used for forecasting time series with trends and seasonality after appropriate preprocessing.