Vertaile menetelmiä

	ARIMA (Autoregressive Integrated Moving Average) -malli	Bayesilainen regressio	Markov-ketju-Monte Carlo (MCMC)
Tieteenala	Ekonometria	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Regression model	Bayesian methods	Bayesian methods
Syntyvuosi	2015	—	—
Kehittäjä	Box & Jenkins (Box-Jenkins methodology)	—	—
Tyyppi	Univariate time-series model	Bayesian linear model	Posterior sampling algorithm
Alkuperäislähde	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
Rinnakkaisnimet	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	bayesian linear regression, probabilistic regression, bayesian regresyon	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Liittyvät	5	2	3
Tiivistelmä	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.