手法を比較

	非線形SARIMAモデル	GARCHモデル（ボラティリティ予測）	SARIMAモデル
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	1990–2000	1986	1970 (first edition); 1976 (revised)
提唱者	Tong (1990) for threshold nonlinear extensions; Franses & van Dijk (2000) for empirical finance applications	Tim Bollerslev	Box, Jenkins, and Reinsel
種類	Nonlinear time series model	Conditional volatility model	Seasonal time series model
原典	Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 978-0198523000	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
別名	NL-SARIMA, nonlinear seasonal ARIMA, threshold SARIMA, smooth transition SARIMA	GARCH, GARCH(1,1), conditional volatility model, GARCH Modeli (Oynaklık Tahmini)	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
関連	3	5	5
概要	The Nonlinear SARIMA model extends the classical Seasonal ARIMA framework by replacing the linear conditional mean function with a nonlinear specification — such as threshold switching or smooth transition — while retaining seasonal differencing and lag structure. It is used when seasonal time series exhibit regime-dependent dynamics, asymmetric adjustment, or other nonlinear patterns that a linear model cannot capture.	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.	SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse for univariate seasonal time series forecasting in econometrics, economics, and official statistics.