เปรียบเทียบวิธี

	แบบจำลองออโตริเกรสซีฟไม่เชิงเส้น (Nonlinear Autoregressive - NAR)	แบบจำลอง ARMA (Autoregressive Moving Average)	แบบจำลอง ARDL ไม่เชิงเส้น (NARDL)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model
ปีกำเนิด	1978-1990	1970	2014
ผู้ริเริ่ม	Tong, H. (threshold AR); Terasvirta, T. (STAR variant)	George E. P. Box and Gwilym M. Jenkins	Shin, Yu & Greenwood-Nimmo
ประเภท	Nonlinear time series model	Time series model	Nonlinear cointegration model
แหล่งต้นตำรับ	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.
ชื่อเรียกอื่น	NAR model, nonlinear autoregression, NLAR, threshold autoregressive model	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
ที่เกี่ยวข้อง	6	5	5
สรุป	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 ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting.	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.