Linganisha mbinu

	Nadharia ya Thamani Iliyokithiri (EVT)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Thibitisho la Thamani ya Hatari (Matarajio ya Upungufu)	Exponential GARCH (EGARCH)
Nyanja	Fedha	Ekonometriki	Fedha	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	2001	2015	2000	1991
Mwanzilishi	Coles (textbook treatment); McNeil, Frey & Embrechts	Box & Jenkins (Box-Jenkins methodology)	Rockafellar & Uryasev (2000); Acerbi & Tasche (2002)	Nelson
Aina	Tail / extreme-event model	Univariate time-series model	Coherent tail-risk measure	Conditional volatility model (asymmetric GARCH variant)
Chanzo asilia	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	Rockafellar, R. T. & Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk, 2(3), 21-41.	Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.
Majina mbadala	EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	CVaR, expected shortfall, average value-at-risk, tail VaR	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH
Zinazohusiana	5	5	5	4
Muhtasari	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).	Conditional Value-at-Risk (CVaR), also called Expected Shortfall, is a coherent tail-risk measure that quantifies the conditional expectation of losses beyond the Value-at-Risk threshold. It was introduced for optimization by Rockafellar and Uryasev (2000) and shown to be coherent by Acerbi and Tasche (2002), and it has replaced VaR as the regulatory standard under Basel III/IV.	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.