Сравнение методов

	Модель ARMA (авторегрессионная скользящая средняя)	Модель ARIMA (авторегрессионная интегрированная скользящая средняя)	Авторегрессионная модель (AR)	Модель SARIMA
Область	Эконометрика	Эконометрика	Эконометрика	Эконометрика
Семейство	Regression model	Regression model	Regression model	Regression model
Год появления	1970	1970	1970s (popularised 1976)	1970 (first edition); 1976 (revised)
Автор метода	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Box, Jenkins, and Reinsel
Тип	Time series model	Time series forecasting model	Time series model	Seasonal time series model
Основополагающий источник	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. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
Другие названия	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	AR model, AR(p) model, autoregression, AR process	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Связанные	5	6	6	5
Сводка	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.	An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial series.	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.