Vertaile menetelmiä

	Bayesiläinen ARMA-malli	Bayesiläinen ARIMA-malli
Tieteenala	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model
Syntyvuosi	1970s–1980s	1970s (ARIMA); Bayesian extension prominent from 1990s
Kehittäjä	Box & Jenkins (classical ARMA); Bayesian treatment developed through work of Zellner, Geweke, and others in 1970s–1980s	Pole, West & Harrison (Bayesian treatment); Box & Jenkins (ARIMA foundation)
Tyyppi	Bayesian time series model	Bayesian time series model
Alkuperäislähde	Geweke, J., & Meese, R. (1981). Estimating regression models of finite but unknown order. International Economic Review, 22(1), 55–70.	Pole, A., West, M., & Harrison, J. (1994). Applied Bayesian Forecasting and Time Series Analysis. Chapman & Hall. ISBN: 978-0412416903
Rinnakkaisnimet	Bayesian ARMA, B-ARMA, Bayesian autoregressive moving average, ARMA with Bayesian inference	Bayesian ARIMA, BARIMA, Bayesian Box-Jenkins model, Bayesian integrated time series model
Liittyvät	6	6
Tiivistelmä	The Bayesian ARMA model applies Bayesian inference to the classical autoregressive moving average framework for stationary univariate time series. Rather than producing single point estimates for the AR and MA parameters, it yields full posterior distributions, naturally incorporating prior knowledge and providing coherent uncertainty quantification over forecasts and impulse responses.	The Bayesian ARIMA model combines the classical Box-Jenkins ARIMA framework with Bayesian inference. Instead of obtaining single point estimates for autoregressive and moving average parameters, it places prior distributions over them and uses observed data to update beliefs into a full posterior distribution, enabling coherent uncertainty quantification and probabilistic forecasting.