Linganisha mbinu

	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Muundo wa Autoregressive (AR)	Mfumo wa SARIMA
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1970	1970s (popularised 1976)	1970 (first edition); 1976 (revised)
Mwanzilishi	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Box, Jenkins, and Reinsel
Aina	Time series forecasting model	Time series model	Seasonal time series model
Chanzo asilia	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
Majina mbadala	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	AR model, AR(p) model, autoregression, AR process	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Zinazohusiana	6	6	5
Muhtasari	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.	An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial series.	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.