विधियों की तुलना करें

	वेक्टर एरर करेक्शन मॉडल (VECM)	ARDL सीमा परीक्षण (Pesaran सीमा परीक्षण)	ऑटोरेग्रेसिव इंटीग्रेटेड मूविंग एवरेज (ARIMA) मॉडल	साधारण न्यूनतम वर्ग (OLS) समाश्रयण
क्षेत्र	अर्थमिति	अर्थमिति	अर्थमिति	अर्थमिति
परिवार	Regression model	Regression model	Regression model	Regression model
उद्भव वर्ष	1987	2001	2015	2019
प्रवर्तक	Engle & Granger	Pesaran, Shin & Smith	Box & Jenkins (Box-Jenkins methodology)	Wooldridge (textbook treatment); classical least squares
प्रकार	Multivariate time-series model	Cointegration test / Autoregressive distributed lag model	Univariate time-series model	Linear regression
मौलिक स्रोत	Engle, R. F. & Granger, C. W. J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251-276.	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.	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
उपनाम	vector error correction model, error correction model, cointegration model, VECM (Vektör Hata Düzeltme Modeli)	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
संबंधित	4	4	5	5
सारांश	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.	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.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	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).