เปรียบเทียบวิธี

	โมเดล Robust ARMA	แบบจำลอง ARIMA (Autoregressive Integrated Moving Average)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model
ปีกำเนิด	1986	1970
ผู้ริเริ่ม	Martin & Yohai (1986); broader robust time series literature	George Box and Gwilym Jenkins
ประเภท	Robust time series model	Time series forecasting model
แหล่งต้นตำรับ	Franses, P. H., & Ghijsels, H. (1999). Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15(1), 1-9.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
ชื่อเรียกอื่น	robust ARMA, outlier-robust ARMA, M-estimator ARMA, resistant ARMA estimation	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
ที่เกี่ยวข้อง	5	6
สรุป	The Robust ARMA model extends the classical Autoregressive Moving Average framework by replacing the sensitive least-squares loss with outlier-resistant estimation methods — typically M-estimators or median-based approaches. This protects coefficient estimates and forecasts from being distorted by additive outliers, level shifts, or innovational outliers that are common in economic and financial time series.	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.