مقایسهٔ روش‌ها

	مدل فوریه-ساریمـا	مدل خودرگرسیون برداری فوریه (Fourier VAR Model)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1994	2010s
پدیدآور	Harvey & Scott (1994); Hyndman & Athanasopoulos (popularization)	Enders & Lee; extended by Nazlioglu and others to VAR systems
نوع	Seasonal time series model with trigonometric regressors	Multivariate time-series model
منبع بنیادین	Harvey, A., & Scott, A. (1994). Seasonality in dynamic regression models. The Economic Journal, 104(427), 1324-1345.	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 SARIMA, SARIMA with Fourier terms, Fourier-SARIMA, trigonometric SARIMA	Fourier VAR, smooth structural break VAR, trigonometric VAR, Fourier-augmented VAR
مرتبط	6	6
خلاصه	The Fourier SARIMA model extends the classical Seasonal ARIMA framework by incorporating trigonometric (Fourier) terms as deterministic regressors. This allows the model to approximate smooth, complex, or multiple-frequency seasonal patterns without requiring a full seasonal ARIMA structure for every frequency, making it particularly useful for high-frequency data or series with non-integer or evolving seasonality.	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.