विधियों की तुलना करें

	मजबूत ऑटोरेग्रेसिव मॉडल	ऑटोरेग्रेसिव इंटीग्रेटेड मूविंग एवरेज (ARIMA) मॉडल	ARMA मॉडल (ऑटोरिग्रेसिव मूविंग एवरेज)
क्षेत्र	अर्थमिति	अर्थमिति	अर्थमिति
परिवार	Regression model	Regression model	Regression model
उद्भव वर्ष	1986	1970	1970
प्रवर्तक	Martin & Yohai (influential early work); broader robust time series literature	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins
प्रकार	Robust time series model	Time series forecasting model	Time series model
मौलिक स्रोत	Martin, R. D., & Yohai, V. J. (1986). Influence functionals for time series. Annals of Statistics, 14(3), 781–818.	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.
उपनाम	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)
संबंधित	6	6	5
सारांश	The robust AR model fits an autoregressive time series specification using estimation methods — typically M-estimators or bounded-influence estimators — that resist distortion from outliers and heavy-tailed error distributions. Unlike OLS-based AR estimation, robust variants down-weight extreme observations so that a small number of contaminated data points cannot dominate the fitted dynamics.	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.