Vertaile menetelmiä

	Bayesiläinen rakenteellinen aikasarja	ARIMA (Autoregressive Integrated Moving Average) -malli	Markov-ketju-Monte Carlo (MCMC)
Tieteenala	Bayesilainen tilastotiede	Ekonometria	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Regression model	Bayesian methods
Syntyvuosi	2014	2015	—
Kehittäjä	Scott & Varian (2014); Brodersen et al. (2015)	Box & Jenkins (Box-Jenkins methodology)	—
Tyyppi	State-space model / Bayesian structural model	Univariate time-series model	Posterior sampling algorithm
Alkuperäislähde	Scott, S. L. & Varian, H. R. (2014). Predicting the Present with Bayesian Structural Time Series. International Journal of Mathematical Modelling and Numerical Optimisation, 5(1/2), 4–23.	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
Rinnakkaisnimet	BSTS, Bayesian Yapısal Zaman Serisi (BSTS), bayesian state-space model, causal impact model	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Liittyvät	5	5	3
Tiivistelmä	Bayesian Structural Time Series (BSTS) is a state-space modelling framework, introduced by Scott and Varian (2014), that decomposes a time series into additive components — trend, seasonality, and regression — and estimates them jointly through Bayesian inference. It underpins Google's CausalImpact library and is a powerful tool for both forecasting and counterfactual causal analysis of interventions.	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).	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.