مقایسهٔ روش‌ها

	آزمون ARCH-LM برای خوشه‌بندی نوسانات	آزمون بروش-پاگان برای ناهمسانی واریانس	GJR-GARCH (GARCH نامتقارن)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1982	1979	1993
پدیدآور	Robert F. Engle	Trevor Breusch & Adrian Pagan	Glosten, Jagannathan & Runkle (1993); Zakoian (1994)
نوع	Lagrange multiplier diagnostic test for conditional heteroscedasticity	Lagrange-multiplier test for heteroskedasticity	Asymmetric conditional volatility model
منبع بنیادین	Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.	Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287–1294.	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.
نام‌های دیگر	ARCH-LM Testi ve Volatilite Kümelenmesi Analizi, ARCH LM test, Engle's ARCH test, test for autoregressive conditional heteroscedasticity	BP test, Breusch-Pagan-Godfrey test, Lagrange multiplier test for heteroskedasticity, Breusch-Pagan değişen varyans testi	asymmetric GARCH, leverage GARCH, TGARCH, GJR-GARCH — Asimetrik GARCH (Glosten-Jagannathan-Runkle)
مرتبط	6	3	5
خلاصه	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.	The Breusch-Pagan test, introduced by Trevor Breusch and Adrian Pagan in 1979, is a Lagrange-multiplier test for heteroskedasticity — the condition where the variance of a regression's errors changes with the explanatory variables. It works by regressing the squared OLS residuals on candidate variables and checking whether they explain any of the residual variation, signalling that the constant-variance assumption is violated.	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).