Vertaile menetelmiä

	Realisoitu volatiliteetti ja HAR-malli	ARIMA (Autoregressive Integrated Moving Average) -malli	Johansenin kointegraatiotesti ja vektorikorjausmalli	Pitkän muistin mallit (ARFIMA, FIGARCH)
Tieteenala	Rahoitus	Ekonometria	Rahoitus	Rahoitus
Menetelmäperhe	Regression model	Regression model	Regression model	Regression model
Syntyvuosi	2009	2015	1991	1980
Kehittäjä	Corsi (HAR model); Andersen, Bollerslev, Diebold & Labys (realized volatility)	Box & Jenkins (Box-Jenkins methodology)	Søren Johansen	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)
Tyyppi	Time-series regression of realized variance	Univariate time-series model	Multivariate cointegration / vector error correction model	Fractionally integrated time series model
Alkuperäislähde	Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174-196.	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.
Rinnakkaisnimet	realized variance, HAR model, heterogeneous autoregressive model of realized volatility, HAR-RV	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
Liittyvät	5	5	3	4
Tiivistelmä	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.	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.