مقایسهٔ روش‌ها

	مدل تصحیح خطای برداری فوریه (Fourier VECM)	مدل خودرگرسیون برداری فوریه (Fourier VAR Model)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2004–2012	2010s
پدیدآور	Enders & Lee (2004/2012); extended to VECM by subsequent authors	Enders & Lee; extended by Nazlioglu and others to VAR systems
نوع	Error-correction model with Fourier terms	Multivariate time-series model
منبع بنیادین	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.
نام‌های دیگر	Fourier VECM, Fourier-approximation VECM, smooth-break VECM, trigonometric VECM	Fourier VAR, smooth structural break VAR, trigonometric VAR, Fourier-augmented VAR
مرتبط	5	6
خلاصه	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.