Linganisha mbinu

	Muundo wa Uhusiano wa Kiotomatiki wa Vecta (VAR)	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Urejeshaji wa Njia ya Viwango Vidogo vya Kawaida (OLS)	Kielelezo cha Usahihishaji Hitilafu cha Kivekta (VECM)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	2005	2001	2015	2019	1987
Mwanzilishi	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition	Pesaran, Shin & Smith	Box & Jenkins (Box-Jenkins methodology)	Wooldridge (textbook treatment); classical least squares	Engle & Granger
Aina	Multivariate time-series model	Cointegration test / Autoregressive distributed lag model	Univariate time-series model	Linear regression	Multivariate time-series model
Chanzo asilia	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	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	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	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	4	5	5	4
Muhtasari	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).	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.