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| Modello a Vettore di Correzione d'Errore di Fourier (Fourier VECM)× | Modello VAR di Fourier× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 2004–2012 | 2010s |
| Ideatore≠ | Enders & Lee (2004/2012); extended to VECM by subsequent authors | Enders & Lee; extended by Nazlioglu and others to VAR systems |
| Tipo≠ | Error-correction model with Fourier terms | Multivariate 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., & 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 ↗ |
| Alias | Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM | Fourier VAR, smooth structural break VAR, trigonometric VAR, Fourier-augmented VAR |
| Correlati≠ | 5 | 6 |
| 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 Fourier VAR model extends the standard Vector Autoregression by replacing fixed deterministic terms with Fourier trigonometric components, allowing the intercept (and optionally the trend) to shift gradually and smoothly over time. This eliminates the need to pre-specify the number, timing, or shape of structural breaks in a multivariate time-series system. |
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