Vertaile menetelmiä

	Liukuvan keskiarvon (MA) malli	ARIMA-malli (Autoregressiivinen integroitu liukuva keskiarvo)	ARMA-malli (Autoregressiivinen liikkuva keskiarvo)	SARIMA-malli
Tieteenala	Ekonometria	Ekonometria	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model	Regression model	Regression model
Syntyvuosi	1970	1970	1970	1970 (first edition); 1976 (revised)
Kehittäjä	Box and Jenkins	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Box, Jenkins, and Reinsel
Tyyppi	Linear time series model	Time series forecasting model	Time series model	Seasonal time series model
Alkuperäislähde	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744	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	MA model, MA(q) process, moving-average process, Box-Jenkins MA	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Liittyvät	5	6	5	5
Tiivistelmä	The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itself, the MA model uses lagged error terms, making it well-suited for capturing short-lived disturbances that dissipate over q periods.	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.	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.	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.