مقایسهٔ روش‌ها

	مدل پارامتر زمان-متغیر NARDL (TVP-NARDL)	آزمون حدود ARDL (آزمون حدود پزاران)	مدل خودرگرسیونی تأخیر توزیع غیرخطی (NARDL)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2019 (TVP extension); 2014 (NARDL base)	2001	2014
پدیدآور	Bagnai & Ospina-Rojas (TVP extension); NARDL base by Shin, Yu & Greenwood-Nimmo	Pesaran, Shin & Smith	Shin, Yu & Greenwood-Nimmo
نوع	Nonlinear time-series model with time-varying coefficients	Cointegration test / Autoregressive distributed lag model	Asymmetric cointegration / error-correction model
منبع بنیادین	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In W. Horrace & R. Sickles (Eds.), Festschrift in Honor of Peter Schmidt (pp. 281–314). Springer.	Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics, 16(3), 289–326.	Shin, Y., Yu, B. & Greenwood-Nimmo, M. (2014). Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework. In: Sickles, R. & Horrace, W. (Eds.), Festschrift in Honor of Peter Schmidt. Springer.
نام‌های دیگر	TVP-NARDL, time-varying NARDL, rolling NARDL, dynamic asymmetric ARDL	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	nonlinear ARDL, asymmetric ARDL, Doğrusal Olmayan ARDL (NARDL)
مرتبط	3	4	4
خلاصه	The Time-Varying Parameter NARDL (TVP-NARDL) model extends the Nonlinear ARDL framework by allowing the coefficients on positive and negative partial sums of a regressor to change over time. This combination captures both asymmetric responses and structural instability in long-run and short-run relationships within a single cointegrating specification.	The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains valid whether the variables are I(0), I(1) or a mix of the two, and it is more reliable than Johansen in small samples of roughly 30 to 80 observations.	The NARDL model, introduced by Shin, Yu and Greenwood-Nimmo in 2014, extends the ARDL framework to capture asymmetric long-run and short-run relationships, testing whether positive and negative changes in a regressor affect the dependent variable differently.