手法を比較

	長期記憶モデル（ARFIMA、FIGARCH）	ARIMA（自己回帰和分移動平均）モデル	GARCHモデル（ボラティリティ予測）
分野	ファイナンス	計量経済学	計量経済学
系統	Regression model	Regression model	Regression model
提唱年	1980	2015	1986
提唱者	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)	Box & Jenkins (Box-Jenkins methodology)	Tim Bollerslev
種類	Fractionally integrated time series model	Univariate time-series model	Conditional volatility model
原典	Granger, C. W. J. & Joyeux, R. (1980). An Introduction to Long-Memory Time Series Models and Fractional Differencing. Journal of Time Series Analysis, 1(1), 15-29.	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
別名	ARFIMA, FIGARCH, fractionally integrated models, fractional integration	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	GARCH, GARCH(1,1), conditional volatility model, GARCH Modeli (Oynaklık Tahmini)
関連	4	5	5
概要	Long-memory models are fractional-integration methods that capture genuine long memory through a hyperbolically decaying autocorrelation structure. ARFIMA, introduced by Granger and Joyeux (1980), models long memory in return series, while FIGARCH, introduced by Baillie, Bollerslev and Mikkelsen (1996), captures long memory in volatility series; the parameter d measures the degree of fractional integration.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, introduced by Tim Bollerslev in 1986, models the time-varying conditional variance of a financial time series. It captures volatility clustering and the ARCH effect, and is the standard tool for estimating risk and volatility in return series.