Linganisha mbinu

	Modeli wa Wastani unaosonga (MA) wa mpangilio q	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	Box and Jenkins	George E. P. Box and Gwilym M. Jenkins	Box, Jenkins, and Reinsel
Aina	Linear time series model	Time series model	Seasonal time series model
Chanzo asilia	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744	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	MA model, MA(q) process, moving-average process, Box-Jenkins MA	AR model, AR(p) model, autoregression, AR process	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Zinazohusiana	5	6	5
Muhtasari	The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itself, the MA model uses lagged error terms, making it well-suited for capturing short-lived disturbances that dissipate over q periods.	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.