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| Модел ARIMA (Autoregressive Integrated Moving Average)× | Байесов регресионен модел× | Марковски Монте Карло вериги (MCMC)× | |
|---|---|---|---|
| Област≠ | Иконометрия | Бейсови методи | Бейсови методи |
| Семейство≠ | Regression model | Bayesian methods | Bayesian methods |
| Година на възникване≠ | 2015 | — | — |
| Създател≠ | Box & Jenkins (Box-Jenkins methodology) | — | — |
| Тип≠ | Univariate time-series model | Bayesian linear model | Posterior sampling algorithm |
| Основополагащ източник≠ | 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 |
| Други названия | 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) |
| Свързани≠ | 5 | 2 | 3 |
| Резюме≠ | 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. |
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