Linganisha mbinu

	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Urejeshaji wa Njia ya Viwango Vidogo vya Kawaida (OLS)	Kielelezo cha Usahihishaji Hitilafu cha Kivekta (VECM)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2001	2019	1987
Mwanzilishi	Pesaran, Shin & Smith	Wooldridge (textbook treatment); classical least squares	Engle & Granger
Aina	Cointegration test / Autoregressive distributed lag model	Linear regression	Multivariate time-series model
Chanzo asilia	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	Engle, R. F. & Granger, C. W. J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251-276.
Majina mbadala	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	vector error correction model, error correction model, cointegration model, VECM (Vektör Hata Düzeltme Modeli)
Zinazohusiana	4	5	4
Muhtasari	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).	The Vector Error Correction Model is a multivariate time-series model for cointegrated series that captures both their short-run dynamics and their long-run equilibrium relationship. It was introduced by Engle and Granger in 1987 as part of the cointegration and error-correction framework.