Порівняння методів

	Нелінійна модель ARIMA	Модель ARIMA (Авторегресійна інтегрована ковзна середня)	Модель GARCH (Прогнозування волатильності)
Галузь	Економетрика	Економетрика	Економетрика
Родина	Regression model	Regression model	Regression model
Рік появи	1978-1994	1970	1986
Автор методу	Howell Tong (SETAR/TAR framework); Timo Terasvirta (STAR extensions)	George Box and Gwilym Jenkins	Tim Bollerslev
Тип	Nonlinear time series model	Time series forecasting model	Conditional volatility model
Основоположне джерело	Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 9780198522249	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
Інші назви	nonlinear ARIMA, NARIMA, nonlinear time series model, nonlinear Box-Jenkins model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	GARCH, GARCH(1,1), conditional volatility model, GARCH Modeli (Oynaklık Tahmini)
Пов'язані	3	6	5
Підсумок	The Nonlinear ARIMA model extends the classical Box-Jenkins ARIMA framework by allowing the conditional mean of a time series to depend on past values and past errors through a nonlinear function. It encompasses families such as Threshold AR (TAR/SETAR), Smooth Transition AR (STAR/LSTAR/ESTAR), and Markov-switching models, capturing asymmetric dynamics, regime changes, and business-cycle asymmetries that linear ARIMA cannot represent.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	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.