Linganisha mbinu

	Mfumo Imara wa ARIMA	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1986–1993	1970
Mwanzilishi	Tsay (1986); Chen & Liu (1993)	George Box and Gwilym Jenkins
Aina	Robust time series model	Time series forecasting model
Chanzo asilia	Tsay, R. S. (1986). Time series model specification in the presence of outliers. Journal of the American Statistical Association, 81(393), 132–141.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Majina mbadala	robust ARIMA, outlier-resistant ARIMA, robust time series estimation, ARIMA with outlier detection	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
Zinazohusiana	4	6
Muhtasari	Robust ARIMA extends the classical ARIMA framework to detect and correct the influence of outliers and structural breaks during estimation. By jointly identifying anomalous observations and re-estimating model parameters, it produces coefficient estimates and forecasts that are far less distorted by isolated shocks or data errors than standard ARIMA.	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.