เปรียบเทียบวิธี

	การทดสอบ ARCH-LM สำหรับการรวมกลุ่มของความผันผวน	การทดสอบ Breusch-Pagan สำหรับความแปรปรวนต่างกัน	แบบจำลองความแปรปรวนแบบมีเงื่อนไขอัตถอยทั่วไป (GARCH)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model
ปีกำเนิด	1982	1979	1986
ผู้ริเริ่ม	Robert F. Engle	Trevor Breusch & Adrian Pagan	Tim Bollerslev
ประเภท	Lagrange multiplier diagnostic test for conditional heteroscedasticity	Lagrange-multiplier test for heteroskedasticity	Conditional volatility model
แหล่งต้นตำรับ	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.	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
ชื่อเรียกอื่น	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	GARCH(1,1), generalized ARCH, conditional volatility model, GARCH Modeli
ที่เกี่ยวข้อง	6	3	5
สรุป	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.	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.