เปรียบเทียบวิธี

	แบบจำลอง Robust Nonlinear Autoregressive Distributed Lag (Robust NARDL)	การทดสอบขอบเขต ARDL (การทดสอบขอบเขต Pesaran)	การถดถอยกำลังสองน้อยที่สุดสามัญ (OLS)	การถดถอยควอนไทล์
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model	Regression model
ปีกำเนิด	2014–2020s	2001	2019	1978
ผู้ริเริ่ม	Extension of Shin, Yu & Greenwood-Nimmo (2014) NARDL framework with robust (outlier-resistant) estimation	Pesaran, Shin & Smith	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett
ประเภท	Nonlinear time-series regression with robust estimation	Cointegration test / Autoregressive distributed lag model	Linear regression	Conditional quantile regression
แหล่งต้นตำรับ	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In W. C. Horrace & R. C. 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.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
ชื่อเรียกอื่น	Robust Nonlinear ARDL, Outlier-Robust NARDL, Robust Asymmetric ARDL, R-NARDL	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	conditional quantile regression, regression quantiles, Kantil Regresyon
ที่เกี่ยวข้อง	3	4	5	5
สรุป	Robust NARDL marries the asymmetric cointegration framework of Shin, Yu, and Greenwood-Nimmo (2014) with outlier-resistant estimation. It decomposes a regressor into positive and negative partial sums, tests for asymmetric long-run relationships via a bounds test, and replaces the OLS criterion with an M- or MM-estimator to guard against leverage points and additive outliers common in macroeconomic and financial time series.	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.