Сравнение методов

	Робастная авторегрессионная модель	Модель ARIMA (авторегрессионная интегрированная скользящая средняя)	Модель ARMA (авторегрессионная скользящая средняя)	Робастный обобщенный метод наименьших квадратов (Robust GLS)
Область	Эконометрика	Эконометрика	Эконометрика	Эконометрика
Семейство	Regression model	Regression model	Regression model	Regression model
Год появления	1986	1970	1970	1936 / 1980
Автор метода	Martin & Yohai (influential early work); broader robust time series literature	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Aitken (GLS theory, 1936); White (robust covariance, 1980)
Тип	Robust time series model	Time series forecasting model	Time series model	Robust linear regression
Основополагающий источник	Martin, R. D., & Yohai, V. J. (1986). Influence functionals for time series. Annals of Statistics, 14(3), 781–818.	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
Другие названия	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	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
Связанные	6	6	5	5
Сводка	The robust AR model fits an autoregressive time series specification using estimation methods — typically M-estimators or bounded-influence estimators — that resist distortion from outliers and heavy-tailed error distributions. Unlike OLS-based AR estimation, robust variants down-weight extreme observations so that a small number of contaminated data points cannot dominate the fitted dynamics.	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.