Das Autoregressiv Integrated Gleitender Durchschnitt (ARIMA) Modell ist eine beliebte statistische Methode, die zur Analyse und forecasting Zeitreihe data. It combines three key components: autoregression (AR), differencing (I), and moving average (MA).
Das 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 lineare Kombination 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 gleitender Durchschnitt 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 ist die Größe des gleitenden Durchschnittsfensters.
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 macht es zu einem Grundpfeiler im Bereich der Zeitreihenprognose.