Linganisha mbinu

	Mfumo Imara wa SARIMA	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1979–2009	1970
Mwanzilishi	Muler, Peña & Yohai (robust ARMA); earlier foundation by Denby & Martin (1979)	George Box and Gwilym Jenkins
Aina	Robust time-series model	Time series forecasting model
Chanzo asilia	Muler, N., Peña, D., & Yohai, V. J. (2009). Robust estimation for ARMA models. The Annals of Statistics, 37(2), 816–840.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Majina mbadala	robust SARIMA, outlier-resistant SARIMA, robust seasonal ARIMA, M-estimator SARIMA	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
Zinazohusiana	4	6
Muhtasari	Robust SARIMA extends the classical Seasonal ARIMA framework by replacing the standard least-squares criterion with a robust loss function — such as an M-estimator — so that outliers and heavy-tailed innovations in seasonal time series cannot distort parameter estimates or invalidate forecasts.	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.