El Autoregresivo Integrated Promedio Móvil (ARIMA) el modelo es un método estadístico popular utilizado para analizar y forecasting series temporales data. It combines three key components: autoregression (AR), differencing (I), and moving average (MA).
El autoregressive part of the model indicates that the current value of the series is based on its past values. This is mathematically expressed as a combinación lineal of previous observations. The integrated component refers to the differencing of raw observations to allow for the time series to become stationary, meaning its statistical properties do not change over time. Finally, the promedio móvil component involves modeling the error term as a linear combination of previous error terms.
ARIMA is particularly useful for non-seasonal time series that exhibit patterns over time, making it an effective tool for forecasting in various fields such as finance, economics, and environmental studies. The model is denoted as ARIMA(p, d, q), where p represents the number of lag observations included in the model (the order of the autoregressive part), d is the degree of differencing (the number of times the data have had past values subtracted), and q es el tamaño de la ventana de media móvil.
ARIMA models can be enhanced further by incorporating seasonal effects, in which case they are referred to as Seasonal ARIMA (SARIMA). The versatility and effectiveness of ARIMA in handling various time series data have made lo convierte en una piedra angular en el campo de la predicción de series temporales.