Linganisha mbinu

	Mfumo wa Fourier AR	Kielelezo cha Usahihishaji wa Hitilafu wa Vecta wa Fourier (Fourier VECM)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	2012	2004–2012
Mwanzilishi	Enders & Lee	Enders & Lee (2004/2012); extended to VECM by subsequent authors
Aina	Time series model with Fourier augmentation	Error-correction model with Fourier terms
Chanzo asilia	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.
Majina mbadala	Fourier AR, trigonometric AR model, smooth transition AR with Fourier terms, FAR model	Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM
Zinazohusiana	6	5
Muhtasari	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.