مقایسهٔ روش‌ها

	نظریه مقادیر حدی (EVT)	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	مدل نمایی GARCH (EGARCH)
حوزه	مالی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2001	2015	1991
پدیدآور	Coles (textbook treatment); McNeil, Frey & Embrechts	Box & Jenkins (Box-Jenkins methodology)	Nelson
نوع	Tail / extreme-event model	Univariate time-series model	Conditional volatility model (asymmetric GARCH variant)
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.
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
مرتبط	5	5	4
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.