Linganisha mbinu

	Modeli ya TGARCH (Threshold GARCH)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Mchambuko wa DCC-GARCH (Dynamic Conditional Correlation)	Modeli ya EGARCH (Exponential GARCH)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	1993-1994	1970	2002	1991
Mwanzilishi	Zakoian (1994); Glosten, Jagannathan & Runkle (1993)	George Box and Gwilym Jenkins	Robert F. Engle	Daniel B. Nelson
Aina	Asymmetric volatility model	Time series forecasting model	Multivariate volatility model	Volatility / conditional variance model
Chanzo asilia	Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931-955.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics, 20(3), 339-350.	Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370.
Majina mbadala	Threshold GARCH, TGARCH, GJR-GARCH, asymmetric GARCH	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	DCC-GARCH, Dynamic Conditional Correlation GARCH, Engle DCC model, multivariate DCC	Exponential GARCH, EGARCH, Nelson EGARCH, log-GARCH
Zinazohusiana	6	6	5	6
Muhtasari	The Threshold GARCH (TGARCH) model extends the standard GARCH framework by allowing positive and negative return shocks to have asymmetric effects on conditional variance. Negative shocks — bad news — typically amplify volatility more than positive shocks of the same magnitude, a stylised fact known as the leverage effect. TGARCH captures this asymmetry through a threshold indicator that switches on when the previous period's shock was negative.	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.	The DCC-GARCH model, introduced by Engle (2002), extends univariate GARCH to capture time-varying correlations between multiple financial time series. It decomposes the multivariate conditional covariance matrix into individual volatility processes and a dynamic correlation matrix, allowing correlations to fluctuate over time while remaining computationally tractable even with many series.	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.