Vertaile menetelmiä

	Robust ARMA -malli	ARMA-malli (Autoregressiivinen liikkuva keskiarvo)
Tieteenala	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model
Syntyvuosi	1986	1970
Kehittäjä	Martin & Yohai (1986); broader robust time series literature	George E. P. Box and Gwilym M. Jenkins
Tyyppi	Robust time series model	Time series model
Alkuperäislähde	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.
Rinnakkaisnimet	robust ARMA, outlier-robust ARMA, M-estimator ARMA, resistant ARMA estimation	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)
Liittyvät	5	5
Tiivistelmä	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 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.