Linganisha mbinu

	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Mifumo ya kopula (Gaussiani, t, Clayton, Gumbel, Frank)	Exponential GARCH (EGARCH)	Nadharia ya Thamani Iliyokithiri (EVT)
Nyanja	Ekonometriki	Fedha	Ekonometriki	Fedha
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	2015	1959	1991	2001
Mwanzilishi	Box & Jenkins (Box-Jenkins methodology)	Sklar (1959); dependence-concept treatment by Joe (1997)	Nelson	Coles (textbook treatment); McNeil, Frey & Embrechts
Aina	Univariate time-series model	Dependence model	Conditional volatility model (asymmetric GARCH variant)	Tail / extreme-event model
Chanzo asilia	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	Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut Statistique de l'Université de Paris, 8, 229-231.	Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.	Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598
Majina mbadala	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	copulas, dependence copulas, vine copulas, Kopula Modelleri (Gaussian, t, Clayton, Gumbel, Frank)	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH	EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold
Zinazohusiana	5	5	4	5
Muhtasari	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).	Copula models are a family of functions that describe the dependence structure between variables separately from their individual (marginal) distributions. The foundation is Sklar's theorem (1959), which shows that any multivariate distribution can be split into its marginals plus a copula; Joe (1997) developed the modern catalogue of dependence concepts. They are central to portfolio risk and credit modelling.	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.