Linganisha mbinu

	Modeli ya EGARCH (Exponential GARCH)	Muundo wa ARCH (Autoregressive Conditional Heteroskedasticity)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1991	1982	1970
Mwanzilishi	Daniel B. Nelson	Robert F. Engle	George Box and Gwilym Jenkins
Aina	Volatility / conditional variance model	Conditional volatility model	Time series forecasting model
Chanzo asilia	Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370.	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Majina mbadala	Exponential GARCH, EGARCH, Nelson EGARCH, log-GARCH	ARCH, autoregressive conditional heteroskedasticity, Engle ARCH, conditional variance model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
Zinazohusiana	6	6	6
Muhtasari	The Exponential GARCH (EGARCH) model, introduced by Nelson (1991), extends the standard GARCH framework by modelling the logarithm of conditional variance. This ensures variance is always positive without parameter constraints and, crucially, allows negative and positive shocks to have asymmetric effects on volatility — capturing the well-known leverage effect in financial markets.	The ARCH model, introduced by Robert Engle in 1982, captures time-varying volatility in financial and macroeconomic time series. It models the conditional variance of today's error as a function of past squared errors, explaining why volatile periods cluster together — a phenomenon known as volatility clustering.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.