مقایسهٔ روش‌ها

	نظریه مقادیر حدی (EVT)	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	مدل نمایی GARCH (EGARCH)	نوسان‌پذیری تحقق‌یافته و مدل HAR
حوزه	مالی	اقتصادسنجی	اقتصادسنجی	مالی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	2001	2015	1991	2009
پدیدآور	Coles (textbook treatment); McNeil, Frey & Embrechts	Box & Jenkins (Box-Jenkins methodology)	Nelson	Corsi (HAR model); Andersen, Bollerslev, Diebold & Labys (realized volatility)
نوع	Tail / extreme-event model	Univariate time-series model	Conditional volatility model (asymmetric GARCH variant)	Time-series regression of realized variance
منبع بنیادین	Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598	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.	Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174-196.
نام‌های دیگر	EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH	realized variance, HAR model, heterogeneous autoregressive model of realized volatility, HAR-RV
مرتبط	5	5	4	5
خلاصه	Extreme Value Theory is a statistical framework for modelling the rare events that live in the tail of a probability distribution. As developed in Coles (2001) and applied to risk by McNeil, Frey & Embrechts (2005), it offers two standard routes: the Generalized Extreme Value (GEV) distribution for block maxima and the Generalized Pareto Distribution (GPD), used in the peaks-over-threshold approach, for exceedances above a high threshold.	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.	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.