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	ARMA मॉडल (ऑटोरिग्रेसिव मूविंग एवरेज)	ऑटोरेग्रेसिव इंटीग्रेटेड मूविंग एवरेज (ARIMA) मॉडल	SARIMA मॉडल
क्षेत्र	अर्थमिति	अर्थमिति	अर्थमिति
परिवार	Regression model	Regression model	Regression model
उद्भव वर्ष	1970	1970	1970 (first edition); 1976 (revised)
प्रवर्तक	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	Box, Jenkins, and Reinsel
प्रकार	Time series model	Time series forecasting model	Seasonal time series model
मौलिक स्रोत	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
उपनाम	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
संबंधित	5	6	5
सारांश	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.