Порівняння методів

	Нелінійна модель SARIMA	Модель GARCH (Прогнозування волатильності)	Модель SARIMA
Галузь	Економетрика	Економетрика	Економетрика
Родина	Regression model	Regression model	Regression model
Рік появи	1990–2000	1986	1970 (first edition); 1976 (revised)
Автор методу	Tong (1990) for threshold nonlinear extensions; Franses & van Dijk (2000) for empirical finance applications	Tim Bollerslev	Box, Jenkins, and Reinsel
Тип	Nonlinear time series model	Conditional volatility model	Seasonal time series model
Основоположне джерело	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
Інші назви	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
Пов'язані	3	5	5
Підсумок	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.