Linganisha mbinu

	Mfumo wa Mabadiliko ya Mazinatio ya Markov (MS-AR / MS-VAR)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Exponential GARCH (EGARCH)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1989	2015	1991
Mwanzilishi	Hamilton (1989); Kim & Nelson (1999)	Box & Jenkins (Box-Jenkins methodology)	Nelson
Aina	Regime-switching time series model	Univariate time-series model	Conditional volatility model (asymmetric GARCH variant)
Chanzo asilia	Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357-384.	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.
Majina mbadala	regime-switching model, Markov-switching autoregression, MS-AR, MS-VAR	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH
Zinazohusiana	5	5	4
Muhtasari	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.	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.