Linganisha mbinu

	Kipimo cha ARCH-LM kwa Makundi ya Kutikisika	Exponential GARCH (EGARCH)	Mfumo wa Mabadiliko ya Mazinatio ya Markov (MS-AR / MS-VAR)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1982	1991	1989
Mwanzilishi	Robert F. Engle	Nelson	Hamilton (1989); Kim & Nelson (1999)
Aina	Lagrange multiplier diagnostic test for conditional heteroscedasticity	Conditional volatility model (asymmetric GARCH variant)	Regime-switching time series model
Chanzo asilia	Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.	Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.	Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357-384.
Majina mbadala	ARCH-LM Testi ve Volatilite Kümelenmesi Analizi, ARCH LM test, Engle's ARCH test, test for autoregressive conditional heteroscedasticity	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH	regime-switching model, Markov-switching autoregression, MS-AR, MS-VAR
Zinazohusiana	6	4	5
Muhtasari	The ARCH-LM test is Robert Engle's (1982) Lagrange multiplier diagnostic for autoregressive conditional heteroscedasticity in the residuals of a fitted time-series model. It checks whether the error variance changes over time and clusters into calm and turbulent periods, and it is the standard pre-test run before fitting a GARCH-family volatility model.	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.	The Markov regime-switching model lets the parameters of a time series change probabilistically across hidden regimes governed by a Markov chain. Introduced by Hamilton (1989) and developed further by Kim and Nelson (1999), it automatically detects business-cycle phases such as expansions and contractions.