Methoden vergleichen

	ARMA-Modell (Autoregressiver gleitender Durchschnitt)	ARIMA-Modell (Autoregressives integriertes gleitendes Durchschnittsmodell)	SARIMA-Modell
Fachgebiet	Ökonometrie	Ökonometrie	Ökonometrie
Familie	Regression model	Regression model	Regression model
Entstehungsjahr	1970	1970	1970 (first edition); 1976 (revised)
Urheber	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	Box, Jenkins, and Reinsel
Typ	Time series model	Time series forecasting model	Seasonal time series model
Wegweisende Quelle	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
Aliasnamen	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Verwandt	5	6	5
Zusammenfassung	The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse for univariate seasonal time series forecasting in econometrics, economics, and official statistics.