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| Modello a Vettore di Correzione d'Errore di Fourier (Fourier VECM)× | Modello di Correzione dell'Errore Vettoriale Non Lineare (Nonlinear VECM)× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 2004–2012 | 1989–1998 |
| Ideatore≠ | Enders & Lee (2004/2012); extended to VECM by subsequent authors | Granger & Lee (1989); Enders & Granger (1998) |
| Tipo≠ | Error-correction model with Fourier terms | Nonlinear time-series model |
| Fonte seminale≠ | Enders, W., & Lee, J. (2012). A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574–599. DOI ↗ | Enders, W., & Granger, C. W. J. (1998). Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3), 304–311. DOI ↗ |
| Alias | Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM | nonlinear VECM, NVECM, threshold VECM, asymmetric VECM |
| Correlati≠ | 5 | 2 |
| Sintesi≠ | The Fourier VECM augments the classical vector error correction model with low-frequency trigonometric terms — sine and cosine components — to capture smooth, gradual structural change in cointegrating relationships without specifying the number or timing of breaks in advance. It is used for multivariate cointegrated systems where long-run equilibria may shift gradually over time. | The Nonlinear VECM extends the standard linear VECM by allowing the speed of adjustment toward long-run equilibrium to differ depending on the sign, magnitude, or regime of deviations from that equilibrium. It captures asymmetric or threshold-driven dynamics in cointegrated time-series systems that a standard VECM would miss. |
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