เปรียบเทียบวิธี

	แบบจำลอง AR ที่ทนทาน (Robust AR Model)	แบบจำลอง ARIMA (Autoregressive Integrated Moving Average)	แบบจำลอง ARMA (Autoregressive Moving Average)	แบบจำลองออโตเรเกรสซีฟ (AR)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model	Regression model
ปีกำเนิด	1986	1970	1970	1970s (popularised 1976)
ผู้ริเริ่ม	Martin & Yohai (influential early work); broader robust time series literature	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	George E. P. Box and Gwilym M. Jenkins
ประเภท	Robust time series model	Time series forecasting model	Time series model	Time series model
แหล่งต้นตำรับ	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.	Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043
ชื่อเรียกอื่น	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)	AR model, AR(p) model, autoregression, AR process
ที่เกี่ยวข้อง	6	6	5	6
สรุป	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.	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.