Description

The ARIMA model is defined by three main parameters: p, d, and q.

AR (p):

The autoregressive component (AR) uses the relationship between an observation and a specific number of previous observations (p) indicating how many past values of the series will be used in the prediction.

Example: An ARIMA(2,0,0) uses the last two values of the series to predict the current one.

I (d):

The integrated component (I) refers to the number of differentiations required to make the time series stationary. Differentiation involves calculating the difference between consecutive observations to remove trends or seasonalities, it represents the number of differentiations needed to make the series stationary.

Example: An ARIMA(0,1,0) indicates a series that needs differentiation to achieve stationarity.

MA (q):

The moving average (MA) component models the relationship between an observation and the residual errors of a moving average model applied to past observations (q) indicating how many past errors will be considered

Example: An ARIMA(0,0,1) uses the error of the previous forecast to predict the current value.

Combination of Parameters (p,d,q)

A complete ARIMA model is described by combining these three parameters, allowing the modeling of different types of time series: ARIMA(1,1,1): Model with an autoregressive term, a differentiation, and a moving average term. ARIMA(0,1,2): Model without autoregressive terms, one differentiation and two terms of moving averages.

Outputs

Table with predictions.