השוואת שיטות

	מבחן ברוש-פייגן להטרוסקדסטיות	מודל אוטורגרסיבי מותנה הטרוסקדסטי (GARCH)	GJR-GARCH (GARCH אסימטרי)
תחום	אקונומטריקה	אקונומטריקה	אקונומטריקה
משפחה	Regression model	Regression model	Regression model
שנת המקור	1979	1986	1993
הוגה השיטה	Trevor Breusch & Adrian Pagan	Tim Bollerslev	Glosten, Jagannathan & Runkle (1993); Zakoian (1994)
סוג	Lagrange-multiplier test for heteroskedasticity	Conditional volatility model	Asymmetric conditional volatility model
מקור מכונן	Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287–1294.	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307-327.	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.
כינויים	BP test, Breusch-Pagan-Godfrey test, Lagrange multiplier test for heteroskedasticity, Breusch-Pagan değişen varyans testi	GARCH(1,1), generalized ARCH, conditional volatility model, GARCH Modeli	asymmetric GARCH, leverage GARCH, TGARCH, GJR-GARCH — Asimetrik GARCH (Glosten-Jagannathan-Runkle)
קשורות	3	5	5
תקציר	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.	GARCH is an econometric model for the time-varying volatility of financial time series, introduced by Tim Bollerslev in 1986 as a generalisation of Engle's ARCH model. It treats the conditional variance as a function of past squared shocks and past variances, capturing the volatility clustering seen in returns.	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).