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	Model nieliniowy ARMA (NARMA)	Model ARCH (Autoregresywna Heteroskedastyczność Warunkowa)	Model ARMA (Autoregresyjny Model Średniej Ruchomej)
Dziedzina	Ekonometria	Ekonometria	Ekonometria
Rodzina	Regression model	Regression model	Regression model
Rok powstania	1980s–1990s	1982	1970
Twórca	Tong (1990); Granger & Terasvirta (1993)	Robert F. Engle	George E. P. Box and Gwilym M. Jenkins
Typ	Nonlinear time series model	Conditional volatility model	Time series model
Źródło pierwotne	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.
Inne nazwy	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)
Pokrewne	2	6	5
Podsumowanie	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.