手法を比較

	ベイズARCHモデル	ベイズGARCHモデル
分野	計量経済学	計量経済学
系統	Regression model	Regression model
提唱年	1982 (ARCH); 1989 (Bayesian estimation)	1989–2000
提唱者	Robert F. Engle (ARCH, 1982); Bayesian treatment: John Geweke (1989)	Geweke (1989); further developed by Nakatsuma (2000) and Bauwens & Lubrano (1998)
種類	Volatility model with Bayesian inference	Bayesian 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.	Geweke, J. (1989). Exact predictive densities for linear models with ARCH disturbances. Journal of Econometrics, 40(1), 63–86.
別名	Bayesian ARCH, ARCH with Bayesian estimation, Bayesian conditional heteroskedasticity model, B-ARCH	Bayesian GARCH, BGARCH, GARCH with Bayesian inference, Bayesian volatility model
関連	6	4
概要	The Bayesian ARCH model estimates Engle's Autoregressive Conditional Heteroskedasticity specification within a Bayesian framework. Instead of maximising a likelihood, it combines a prior distribution over the volatility parameters with the data likelihood to obtain a full posterior distribution, providing richer uncertainty quantification than classical maximum-likelihood ARCH.	The Bayesian GARCH model combines the GARCH framework for time-varying volatility with Bayesian posterior inference. Instead of maximising a likelihood, it specifies prior distributions for the GARCH parameters and draws from the resulting posterior — typically via Markov chain Monte Carlo (MCMC) — to quantify both point estimates and full uncertainty about volatility dynamics.