Сравнение на методи

	Нелинеен SARIMA модел	Модел ARIMA (Авторегресионен интегриран плъзгащ се среден)	Модел GARCH (Прогнозиране на волатилността)	Модел SARIMA
Област	Иконометрия	Иконометрия	Иконометрия	Иконометрия
Семейство	Regression model	Regression model	Regression model	Regression model
Година на възникване	1990–2000	1970	1986	1970 (first edition); 1976 (revised)
Създател	Tong (1990) for threshold nonlinear extensions; Franses & van Dijk (2000) for empirical finance applications	George Box and Gwilym Jenkins	Tim Bollerslev	Box, Jenkins, and Reinsel
Тип	Nonlinear time series model	Time series forecasting model	Conditional volatility model	Seasonal time series model
Основополагащ източник	Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 978-0198523000	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.	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
Други названия	NL-SARIMA, nonlinear seasonal ARIMA, threshold SARIMA, smooth transition SARIMA	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	GARCH, GARCH(1,1), conditional volatility model, GARCH Modeli (Oynaklık Tahmini)	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Свързани	3	6	5	5
Резюме	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 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.	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.