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| Modello AR di Fourier× | Modello a Vettore di Correzione d'Errore di Fourier (Fourier VECM)× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 2012 | 2004–2012 |
| Ideatore≠ | Enders & Lee | Enders & Lee (2004/2012); extended to VECM by subsequent authors |
| Tipo≠ | Time series model with Fourier augmentation | Error-correction model with Fourier terms |
| 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 AR, trigonometric AR model, smooth transition AR with Fourier terms, FAR model | Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM |
| Correlati≠ | 6 | 5 |
| Sintesi≠ | The Fourier AR model extends the standard autoregressive specification by adding trigonometric (sine and cosine) terms to the deterministic component. This allows the model to capture smooth, gradual shifts in the mean or trend of a time series without requiring the researcher to locate or count structural break points explicitly. | 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. |
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