مقایسهٔ روش‌ها

	مدل آریما فوریه	مدل خودرگرسیون برداری فوریه (Fourier VAR Model)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2004–2006	2010s
پدیدآور	Becker, Enders, and Hurn	Enders & Lee; extended by Nazlioglu and others to VAR systems
نوع	Time series model with smooth structural change	Multivariate time-series model
منبع بنیادین	Becker, R., Enders, W., & Hurn, S. (2006). A general test for time dependence in parameters. Journal of Applied Econometrics, 21(7), 1005–1028.	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 ARMA, ARMA with Fourier terms, trigonometric ARMA, smooth structural change ARMA	Fourier VAR, smooth structural break VAR, trigonometric VAR, Fourier-augmented VAR
مرتبط	5	6
خلاصه	The Fourier ARMA model augments the classical Autoregressive Moving Average framework with low-frequency Fourier (sine and cosine) terms to capture smooth, gradual shifts in the mean or trend of a time series. Unlike dummy-variable approaches, it requires no prior knowledge of when structural change occurred, approximating change with flexible trigonometric functions.	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.