So sánh phương pháp

	Mô hình ARIMA phi tuyến tính	Mô hình ARIMA (Autoregressive Integrated Moving Average)	Mô hình Tự hồi quy Vector (VAR)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Regression model
Năm ra đời	1978-1994	1970	2005
Người khởi xướng	Howell Tong (SETAR/TAR framework); Timo Terasvirta (STAR extensions)	George Box and Gwilym Jenkins	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Loại	Nonlinear time series model	Time series forecasting model	Multivariate time-series model
Công trình gốc	Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 9780198522249	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Tên gọi khác	nonlinear ARIMA, NARIMA, nonlinear time series model, nonlinear Box-Jenkins model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Liên quan	3	6	4
Tóm tắt	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 ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	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).