Linganisha mbinu

	Modeli wa Wastani unaosonga (MA) wa mpangilio q	Modeli ya ARMA (Autoregressive Moving Average)	Muundo wa Autoregressive (AR)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1970	1970	1970s (popularised 1976)
Mwanzilishi	Box and Jenkins	George E. P. Box and Gwilym M. Jenkins	George E. P. Box and Gwilym M. Jenkins
Aina	Linear time series model	Time series model	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. (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
Majina mbadala	MA model, MA(q) process, moving-average process, Box-Jenkins MA	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	AR model, AR(p) model, autoregression, AR process
Zinazohusiana	5	5	6
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.	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.	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.