เปรียบเทียบวิธี

	การถดถอยร่วมแบบไม่เชิงเส้นของ Engle-Granger	แบบจำลอง ARDL ไม่เชิงเส้น (NARDL)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model
ปีกำเนิด	1998-2006	2014
ผู้ริเริ่ม	Kapetanios, Shin & Snell; Enders & Granger	Shin, Yu & Greenwood-Nimmo
ประเภท	Cointegration test	Nonlinear cointegration model
แหล่งต้นตำรับ	Kapetanios, G., Shin, Y., & Snell, A. (2006). Testing for cointegration in nonlinear smooth transition error correction models. Econometric Theory, 22(2), 279-303.	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	nonlinear cointegration, threshold cointegration, KSS cointegration, ESTAR cointegration	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
ที่เกี่ยวข้อง	3	5
สรุป	Nonlinear Engle-Granger cointegration extends the classical two-step Engle-Granger procedure to detect long-run equilibria where adjustment toward the equilibrium is nonlinear — for example, faster above than below a threshold, or governed by a smooth transition mechanism. It is widely applied in financial economics, purchasing power parity tests, and commodity price analysis.	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.