Linganisha mbinu

	Mchoro wa Kujirejelea Usio na Mstari (NAR)	Muundo wa Autoregressive (AR)	Mfumo wa ARDL Usiohusisha Mstari (NARDL)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1978-1990	1970s (popularised 1976)	2014
Mwanzilishi	Tong, H. (threshold AR); Terasvirta, T. (STAR variant)	George E. P. Box and Gwilym M. Jenkins	Shin, Yu & Greenwood-Nimmo
Aina	Nonlinear time series model	Time series model	Nonlinear cointegration model
Chanzo asilia	Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 9780198522201	Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Applications (pp. 281–314). Springer.
Majina mbadala	NAR model, nonlinear autoregression, NLAR, threshold autoregressive model	AR model, AR(p) model, autoregression, AR process	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Zinazohusiana	6	6	5
Muhtasari	The Nonlinear AR model extends the classical autoregressive framework by allowing the mapping from past values to the current value to follow an arbitrary or regime-switching nonlinear function. Major families include the Self-Exciting Threshold AR (SETAR), Smooth Transition AR (STAR), and neural network AR, each capturing different forms of asymmetry, regime shifts, or smooth nonlinear dynamics in univariate time series.	An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial series.	The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing the regressor into cumulative positive and negative partial sums, it tests whether increases and decreases in a variable exert different effects on the outcome — a feature especially relevant in financial and energy economics where positive and negative shocks rarely cancel out symmetrically.