Comparer des méthodes

	Modèle ARIMA (Autoregressive Integrated Moving Average)	Test de cointégration de Johansen et modèle à correction d'erreur vectoriel	Modèles à mémoire longue (ARFIMA, FIGARCH)
Domaine	Économétrie	Finance	Finance
Famille	Regression model	Regression model	Regression model
Année d'origine	2015	1991	1980
Auteur d'origine	Box & Jenkins (Box-Jenkins methodology)	Søren Johansen	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)
Type	Univariate time-series model	Multivariate cointegration / vector error correction model	Fractionally integrated time series model
Source fondatrice	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	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.	Granger, C. W. J. & Joyeux, R. (1980). An Introduction to Long-Memory Time Series Models and Fractional Differencing. Journal of Time Series Analysis, 1(1), 15-29.
Alias	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	Johansen test, VECM, vector error correction model, multivariate cointegration	ARFIMA, FIGARCH, fractionally integrated models, fractional integration
Apparentées	5	3	4
Résumé	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).	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.	Long-memory models are fractional-integration methods that capture genuine long memory through a hyperbolically decaying autocorrelation structure. ARFIMA, introduced by Granger and Joyeux (1980), models long memory in return series, while FIGARCH, introduced by Baillie, Bollerslev and Mikkelsen (1996), captures long memory in volatility series; the parameter d measures the degree of fractional integration.