手法を比較

	ARCH-LM検定（ボラティリティ・クラスタリングのため）	一般化自己回帰条件付き分散 (GARCH)	GJR-GARCH（非対称GARCH）
分野	計量経済学	計量経済学	計量経済学
系統	Regression model	Regression model	Regression model
提唱年	1982	1986	1993
提唱者	Robert F. Engle	Tim Bollerslev	Glosten, Jagannathan & Runkle (1993); Zakoian (1994)
種類	Lagrange multiplier diagnostic test for conditional heteroscedasticity	Conditional volatility model	Asymmetric conditional volatility model
原典	Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.	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.
別名	ARCH-LM Testi ve Volatilite Kümelenmesi Analizi, ARCH LM test, Engle's ARCH test, test for autoregressive conditional heteroscedasticity	GARCH(1,1), generalized ARCH, conditional volatility model, GARCH Modeli	asymmetric GARCH, leverage GARCH, TGARCH, GJR-GARCH — Asimetrik GARCH (Glosten-Jagannathan-Runkle)
関連	6	5	5
概要	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.	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).