So sánh phương pháp

	Mô hình Tự hồi quy Phi tuyến (NAR)	Mô hình ARIMA (Autoregressive Integrated Moving Average)	Mô hình ARDL phi tuyến (NARDL)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Regression model
Năm ra đời	1978-1990	1970	2014
Người khởi xướng	Tong, H. (threshold AR); Terasvirta, T. (STAR variant)	George Box and Gwilym Jenkins	Shin, Yu & Greenwood-Nimmo
Loại	Nonlinear time series model	Time series forecasting model	Nonlinear cointegration model
Công trình gốc	Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 9780198522201	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Applications (pp. 281–314). Springer.
Tên gọi khác	NAR model, nonlinear autoregression, NLAR, threshold autoregressive model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Liên quan	6	6	5
Tóm tắt	The Nonlinear AR model extends the classical autoregressive framework by allowing the mapping from past values to the current value to follow an arbitrary or regime-switching nonlinear function. Major families include the Self-Exciting Threshold AR (SETAR), Smooth Transition AR (STAR), and neural network AR, each capturing different forms of asymmetry, regime shifts, or smooth nonlinear dynamics in univariate time series.	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.	The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing the regressor into cumulative positive and negative partial sums, it tests whether increases and decreases in a variable exert different effects on the outcome — a feature especially relevant in financial and energy economics where positive and negative shocks rarely cancel out symmetrically.