เปรียบเทียบวิธี

	แบบจำลอง Vector Autoregression (VAR)	การทดสอบขอบเขต ARDL (การทดสอบขอบเขต Pesaran)	แบบจำลอง ARIMA (Autoregressive Integrated Moving Average)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model
ปีกำเนิด	2005	2001	2015
ผู้ริเริ่ม	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition	Pesaran, Shin & Smith	Box & Jenkins (Box-Jenkins methodology)
ประเภท	Multivariate time-series model	Cointegration test / Autoregressive distributed lag model	Univariate time-series model
แหล่งต้นตำรับ	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. 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.	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
ชื่อเรียกอื่น	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli
ที่เกี่ยวข้อง	4	4	5
สรุป	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).	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).