Methoden vergleichen

	Fourier AR-Modell	Fourier VECM (Fourier Vektor-Fehlerkorrekturmodell)
Fachgebiet	Ökonometrie	Ökonometrie
Familie	Regression model	Regression model
Entstehungsjahr	2012	2004–2012
Urheber	Enders & Lee	Enders & Lee (2004/2012); extended to VECM by subsequent authors
Typ	Time series model with Fourier augmentation	Error-correction model with Fourier terms
Wegweisende Quelle	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.	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.
Aliasnamen	Fourier AR, trigonometric AR model, smooth transition AR with Fourier terms, FAR model	Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM
Verwandt	6	5
Zusammenfassung	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.