手法を比較

	フーリエARモデル	フーリエ誤差修正モデル (Fourier VECM)
分野	計量経済学	計量経済学
系統	Regression model	Regression model
提唱年	2012	2004–2012
提唱者	Enders & Lee	Enders & Lee (2004/2012); extended to VECM by subsequent authors
種類	Time series model with Fourier augmentation	Error-correction model with Fourier terms
原典	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.
別名	Fourier AR, trigonometric AR model, smooth transition AR with Fourier terms, FAR model	Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM
関連	6	5
概要	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.