Vertaile menetelmiä

	ARMA-malli (Autoregressiivinen liikkuva keskiarvo)	ARIMA-malli (Autoregressiivinen integroitu liukuva keskiarvo)	SARIMA-malli
Tieteenala	Ekonometria	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model	Regression model
Syntyvuosi	1970	1970	1970 (first edition); 1976 (revised)
Kehittäjä	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	Box, Jenkins, and Reinsel
Tyyppi	Time series model	Time series forecasting model	Seasonal time series model
Alkuperäislähde	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
Rinnakkaisnimet	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
Liittyvät	5	6	5
Tiivistelmä	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.