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	ऑटोरेग्रेसिव इंटीग्रेटेड मूविंग एवरेज (ARIMA) मॉडल	ARMA मॉडल (ऑटोरिग्रेसिव मूविंग एवरेज)	ग्रेंजर कारणता परीक्षण (Granger Causality Test)
क्षेत्र	अर्थमिति	अर्थमिति	अर्थमिति
परिवार	Regression model	Regression model	Regression model
उद्भव वर्ष	1970	1970	1969
प्रवर्तक	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Clive W. J. Granger
प्रकार	Time series forecasting model	Time series model	Causality test (F-test on VAR)
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.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424–438.
उपनाम	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	Granger test, GC test, predictive causality test, Granger non-causality test
संबंधित	6	5	5
सारांश	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.	The Granger causality test is a statistical hypothesis test that determines whether past values of one time series help predict future values of another, beyond what that series' own past already explains. Introduced by Clive Granger in 1969, it is the standard approach for assessing predictive causality in VAR-based time-series analysis.