Linganisha mbinu
Pitia mbinu ulizochagua bega kwa bega; safu zinazotofautiana zinaangaziwa.
| Nadharia ya Thamani Iliyokithiri (EVT)× | Mfumo wa ARIMA (Autoregressive Integrated Moving Average)× | Thibitisho la Thamani ya Hatari (Matarajio ya Upungufu)× | |
|---|---|---|---|
| Nyanja≠ | Fedha | Ekonometriki | Fedha |
| Familia | Regression model | Regression model | Regression model |
| Mwaka wa asili≠ | 2001 | 2015 | 2000 |
| Mwanzilishi≠ | Coles (textbook treatment); McNeil, Frey & Embrechts | Box & Jenkins (Box-Jenkins methodology) | Rockafellar & Uryasev (2000); Acerbi & Tasche (2002) |
| Aina≠ | Tail / extreme-event model | Univariate time-series model | Coherent tail-risk measure |
| 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. DOI ↗ |
| 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 |
| Zinazohusiana | 5 | 5 | 5 |
| 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. |
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