Linganisha mbinu

	Mundo wa ARMA Usiohusisha Mstari (NARMA)	Muundo wa ARCH (Autoregressive Conditional Heteroskedasticity)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1980s–1990s	1982
Mwanzilishi	Tong (1990); Granger & Terasvirta (1993)	Robert F. Engle
Aina	Nonlinear time series model	Conditional volatility model
Chanzo asilia	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.
Majina mbadala	NARMA, nonlinear ARMA, NLARMA, nonlinear autoregressive moving average	ARCH, autoregressive conditional heteroskedasticity, Engle ARCH, conditional variance model
Zinazohusiana	2	6
Muhtasari	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.