Compara mètodes

	Test de Cointegració de Johansen i Model de Correcció d'Errors Vectorial	Model d'ARIMA (Autoregressive Integrated Moving Average)	Model d'Autoregressió Vectorial (VAR)
Camp	Finances	Econometria	Econometria
Família	Regression model	Regression model	Regression model
Any d'origen	1991	2015	2005
Autor original	Søren Johansen	Box & Jenkins (Box-Jenkins methodology)	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Tipus	Multivariate cointegration / vector error correction model	Univariate time-series model	Multivariate time-series model
Font seminal	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.	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	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Àlies	Johansen test, VECM, vector error correction model, multivariate cointegration	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Relacionats	3	5	4
Resum	The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the series and then builds a Vector Error Correction Model (VECM) to describe the short-run dynamics around that equilibrium.	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).	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).