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| Model ARIMA (Autoregressive Integrated Moving Average)× | Wykładniczy GARCH (EGARCH)× | Teoria wartości ekstremalnych (EVT)× | |
|---|---|---|---|
| Dziedzina≠ | Ekonometria | Ekonometria | Finanse |
| Rodzina | Regression model | Regression model | Regression model |
| Rok powstania≠ | 2015 | 1991 | 2001 |
| Twórca≠ | Box & Jenkins (Box-Jenkins methodology) | Nelson | Coles (textbook treatment); McNeil, Frey & Embrechts |
| Typ≠ | Univariate time-series model | Conditional volatility model (asymmetric GARCH variant) | Tail / extreme-event model |
| Źródło pierwotne≠ | 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. DOI ↗ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 |
| Inne nazwy≠ | Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli | exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold |
| Pokrewne≠ | 5 | 4 | 5 |
| Podsumowanie≠ | 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. | 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. |
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