Linganisha mbinu

	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Modeli ya ARMA (Autoregressive Moving Average)	Generalized Least Squares (GLS) Imara
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1970	1970	1936 / 1980
Mwanzilishi	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Aitken (GLS theory, 1936); White (robust covariance, 1980)
Aina	Time series forecasting model	Time series model	Robust linear regression
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.	Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson. Chapter 9: The Generalized Regression Model and Heteroscedasticity. ISBN: 978-0131395381
Majina mbadala	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	robust generalized least squares, GLS with robust standard errors, heteroscedasticity-consistent GLS, HC-GLS
Zinazohusiana	6	5	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.	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.	Robust GLS extends classical Generalized Least Squares by pairing GLS coefficient estimation with heteroscedasticity- and autocorrelation-consistent (HAC) standard errors, or by using M-estimation within the GLS framework. It corrects for non-spherical errors — heteroscedasticity, autocorrelation, or both — while also guarding inference against misspecification of the error covariance structure.