Порівняння методів

	Модель нелінійної ARMA (NARMA)	Модель АРХ (Авторегресивна умовна гетероскедастичність)	Модель ARMA (авторегресійна ковзна середня)
Галузь	Економетрика	Економетрика	Економетрика
Родина	Regression model	Regression model	Regression model
Рік появи	1980s–1990s	1982	1970
Автор методу	Tong (1990); Granger & Terasvirta (1993)	Robert F. Engle	George E. P. Box and Gwilym M. Jenkins
Тип	Nonlinear time series model	Conditional volatility model	Time series model
Основоположне джерело	Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 978-0198522300	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Інші назви	NARMA, nonlinear ARMA, NLARMA, nonlinear autoregressive moving average	ARCH, autoregressive conditional heteroskedasticity, Engle ARCH, conditional variance model	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)
Пов'язані	2	6	5
Підсумок	The Nonlinear ARMA (NARMA) model extends the classical linear ARMA framework by allowing the conditional mean to depend on past observations and past errors through an arbitrary nonlinear function. It captures complex dynamics — such as regime changes, asymmetric cycles, and threshold effects — that linear models miss, making it valuable for economic and financial time series.	The ARCH model, introduced by Robert Engle in 1982, captures time-varying volatility in financial and macroeconomic time series. It models the conditional variance of today's error as a function of past squared errors, explaining why volatile periods cluster together — a phenomenon known as volatility clustering.	The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting.