مقایسهٔ روش‌ها

	نوسان‌پذیری تحقق‌یافته و مدل HAR	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	مدل نمایی GARCH (EGARCH)	آزمون هم‌انباشتگی یوهانسن و مدل برداری تصحیح خطا
حوزه	مالی	اقتصادسنجی	اقتصادسنجی	مالی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	2009	2015	1991	1991
پدیدآور	Corsi (HAR model); Andersen, Bollerslev, Diebold & Labys (realized volatility)	Box & Jenkins (Box-Jenkins methodology)	Nelson	Søren Johansen
نوع	Time-series regression of realized variance	Univariate time-series model	Conditional volatility model (asymmetric GARCH variant)	Multivariate cointegration / vector error correction model
منبع بنیادین	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	Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.
نام‌های دیگر	realized variance, HAR model, heterogeneous autoregressive model of realized volatility, HAR-RV	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH	Johansen test, VECM, vector error correction model, multivariate cointegration
مرتبط	5	5	4	3
خلاصه	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).	EGARCH is an asymmetric GARCH variant, introduced by Nelson in 1991, that models the leverage effect in which bad news raises volatility more than good news of the same size. It captures the negative-shock asymmetry of financial return series by modelling the logarithm of the conditional variance.	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.