Linganisha mbinu

	Modeli ya ARMA (Autoregressive Moving Average)	Mfumo wa ARIMA (Autoregressive Integrated 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	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins
Aina	Time series model	Time series forecasting model	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. (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	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	AR model, AR(p) model, autoregression, AR process
Zinazohusiana	5	6	6
Muhtasari	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.	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.