Compara mètodes

	Volatilitat realitzada i el model HAR	Test de Cointegració de Johansen i Model de Correcció d'Errors Vectorial	Models de memòria llarga (ARFIMA, FIGARCH)
Camp	Finances	Finances	Finances
Família	Regression model	Regression model	Regression model
Any d'origen	2009	1991	1980
Autor original	Corsi (HAR model); Andersen, Bollerslev, Diebold & Labys (realized volatility)	Søren Johansen	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)
Tipus	Time-series regression of realized variance	Multivariate cointegration / vector error correction model	Fractionally integrated time series model
Font seminal	Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174-196.	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.
Àlies	realized variance, HAR model, heterogeneous autoregressive model of realized volatility, HAR-RV	Johansen test, VECM, vector error correction model, multivariate cointegration	ARFIMA, FIGARCH, fractionally integrated models, fractional integration
Relacionats	5	3	4
Resum	Realized volatility estimates an asset's variance directly from high-frequency intraday returns rather than from a parametric latent process. The Heterogeneous Autoregressive (HAR) model of Corsi (2009), building on the realized-volatility framework of Andersen, Bollerslev, Diebold and Labys (2003), forecasts this measure by combining daily, weekly, and monthly volatility components, and is a strong alternative to GARCH for volatility prediction.	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.