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| Modello ARIMA Bayesiano× | Modello VAR Bayesiano (BVAR)× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 1970s (ARIMA); Bayesian extension prominent from 1990s | 1984 |
| Ideatore≠ | Pole, West & Harrison (Bayesian treatment); Box & Jenkins (ARIMA foundation) | Doan, Litterman & Sims |
| Tipo≠ | Bayesian time series model | Multivariate time-series model |
| Fonte seminale≠ | Pole, A., West, M., & Harrison, J. (1994). Applied Bayesian Forecasting and Time Series Analysis. Chapman & Hall. ISBN: 978-0412416903 | Doan, T., Litterman, R., & Sims, C. (1984). Forecasting and conditional projection using realistic prior distributions. Econometric Reviews, 3(1), 1–100. DOI ↗ |
| Alias | Bayesian ARIMA, BARIMA, Bayesian Box-Jenkins model, Bayesian integrated time series model | BVAR, Bayesian VAR, Bayesian vector autoregressive model, BVAR model |
| Correlati≠ | 6 | 5 |
| Sintesi≠ | 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. | The Bayesian Vector Autoregression (BVAR) model extends the classical VAR framework by incorporating prior beliefs about the model coefficients. Priors — most commonly the Minnesota prior — shrink VAR coefficients toward economically sensible values, dramatically reducing overfitting and improving out-of-sample forecast accuracy even when the number of variables is large. |
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