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| Test di cointegrazione (Johansen / Engle-Granger)× | Modello ARIMA (Autoregressive Integrated Moving Average)× | Modello di Autoregressione Vettoriale (VAR)× | |
|---|---|---|---|
| Campo | Econometria | Econometria | Econometria |
| Famiglia | Regression model | Regression model | Regression model |
| Anno di origine≠ | 1988 | 2015 | 2005 |
| Ideatore≠ | Engle & Granger (1987); Johansen (1988) | Box & Jenkins (Box-Jenkins methodology) | Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition |
| Tipo≠ | Time-series cointegration test | Univariate time-series model | Multivariate time-series model |
| Fonte seminale≠ | Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254. DOI ↗ | 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 | Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer. DOI ↗ |
| Alias≠ | Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger) | Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli | vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon |
| Correlati≠ | 5 | 5 | 4 |
| Sintesi≠ | The cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988). | 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). | Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005). |
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