قارن الطرق

	نموذج الانحدار الذاتي المتجه البايزي (BVAR)	نموذج الانحدار الذاتي المتجه بمتغيرات فورييه (Fourier VAR Model)	نموذج الانحدار الذاتي المتجهي (VAR)
المجال	الاقتصاد القياسي	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1984	2010s	2005
صاحب الطريقة	Doan, Litterman & Sims	Enders & Lee; extended by Nazlioglu and others to VAR systems	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
النوع	Multivariate time-series model	Multivariate time-series model	Multivariate time-series model
المصدر التأسيسي	Doan, T., Litterman, R., & Sims, C. (1984). Forecasting and conditional projection using realistic prior distributions. Econometric Reviews, 3(1), 1–100.	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.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
الأسماء البديلة	BVAR, Bayesian VAR, Bayesian vector autoregressive model, BVAR model	Fourier VAR, smooth structural break VAR, trigonometric VAR, Fourier-augmented VAR	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
ذات صلة	5	6	4
الملخص	The Bayesian Vector Autoregression (BVAR) model extends the classical VAR framework by incorporating prior beliefs about the model coefficients. Priors — most commonly the Minnesota prior — shrink VAR coefficients toward economically sensible values, dramatically reducing overfitting and improving out-of-sample forecast accuracy even when the number of variables is large.	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.	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).