Σύγκριση μεθόδων

	VAR κατωφliού και VAR Ομαλής Μετάβασης (TVAR / STVAR)	Έλεγχος ARCH-LM για Συσταδοποίηση Μεταβλητότητας	GJR-GARCH (Ασύμμετρο GARCH)	Μοντέλο Μαρκοβιανής Εναλλαγής Καθεστώτων (MS-AR / MS-VAR)
Πεδίο	Οικονομετρία	Οικονομετρία	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model	Regression model	Regression model
Έτος προέλευσης	1998	1982	1993	1989
Δημιουργός	Tsay (multivariate threshold modelling)	Robert F. Engle	Glosten, Jagannathan & Runkle (1993); Zakoian (1994)	Hamilton (1989); Kim & Nelson (1999)
Τύπος	Nonlinear multivariate time-series model	Lagrange multiplier diagnostic test for conditional heteroscedasticity	Asymmetric conditional volatility model	Regime-switching time series model
Θεμελιώδης πηγή	Tsay, R. S. (1998). Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93(443), 1188-1202.	Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.	Glosten, L. R., Jagannathan, R. & Runkle, D. E. (1993). On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48(5), 1779-1801.	Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357-384.
Εναλλακτικές ονομασίες	TVAR, STVAR, regime-switching VAR, threshold VAR	ARCH-LM Testi ve Volatilite Kümelenmesi Analizi, ARCH LM test, Engle's ARCH test, test for autoregressive conditional heteroscedasticity	asymmetric GARCH, leverage GARCH, TGARCH, GJR-GARCH — Asimetrik GARCH (Glosten-Jagannathan-Runkle)	regime-switching model, Markov-switching autoregression, MS-AR, MS-VAR
Συναφείς	5	6	5	5
Σύνοψη	Threshold VAR and Smooth-Transition VAR are nonlinear multivariate time-series models in which the coefficients of a vector autoregression switch between regimes according to a threshold variable. Building on Tsay's 1998 treatment of multivariate threshold models, they capture different dynamic structures across phases such as the business cycle, financial crises, or policy differences.	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.	GJR-GARCH is a variant of the GARCH conditional-volatility model that captures the asymmetric effect of negative shocks on volatility using an indicator variable. It was introduced by Glosten, Jagannathan and Runkle (1993), with a closely related threshold formulation by Zakoian (1994).	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.