مقایسهٔ روش‌ها

	مدل ARIMA غیرخطی	مدل GARCH (پیش‌بینی نوسانات)	مدل خودرگرسیون برداری (VAR)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1978-1994	1986	2005
پدیدآور	Howell Tong (SETAR/TAR framework); Timo Terasvirta (STAR extensions)	Tim Bollerslev	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
نوع	Nonlinear time series model	Conditional volatility model	Multivariate time-series model
منبع بنیادین	Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 9780198522249	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
نام‌های دیگر	nonlinear ARIMA, NARIMA, nonlinear time series model, nonlinear Box-Jenkins model	GARCH, GARCH(1,1), conditional volatility model, GARCH Modeli (Oynaklık Tahmini)	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
مرتبط	3	5	4
خلاصه	The Nonlinear ARIMA model extends the classical Box-Jenkins ARIMA framework by allowing the conditional mean of a time series to depend on past values and past errors through a nonlinear function. It encompasses families such as Threshold AR (TAR/SETAR), Smooth Transition AR (STAR/LSTAR/ESTAR), and Markov-switching models, capturing asymmetric dynamics, regime changes, and business-cycle asymmetries that linear ARIMA cannot represent.	The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, introduced by Tim Bollerslev in 1986, models the time-varying conditional variance of a financial time series. It captures volatility clustering and the ARCH effect, and is the standard tool for estimating risk and volatility in return series.	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).