مقایسهٔ روش‌ها

	آزمون ARCH-LM برای خوشه‌بندی نوسانات	آزمون بروش-پاگان برای ناهمسانی واریانس	مدل خودرگرسیون شرطی تعمیم‌یافته ناهمسانی (GARCH)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1982	1979	1986
پدیدآور	Robert F. Engle	Trevor Breusch & Adrian Pagan	Tim Bollerslev
نوع	Lagrange multiplier diagnostic test for conditional heteroscedasticity	Lagrange-multiplier test for heteroskedasticity	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.	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
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	GARCH(1,1), generalized ARCH, conditional volatility model, GARCH Modeli
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.	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.