Linganisha mbinu

	Kipimo cha Mipaka cha Fourier ARDL	Mfumo wa ARDL Usiohusisha Mstari (NARDL)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	2001-2021	2014
Mwanzilishi	Pesaran, Shin & Smith (ARDL foundation); Fourier extension by Nazlioglu and related authors	Shin, Yu & Greenwood-Nimmo
Aina	Cointegration / bounds test	Nonlinear cointegration model
Chanzo asilia	Nazlioglu, S., Gormus, A., & Soytas, U. (2021). Oil prices and monetary policy in emerging markets: structural breaks, asymmetries, and Fourier approximations. Energy Economics, 95, 105119.	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	Fourier ARDL, Fourier bounds testing, ARDL with Fourier approximation, F-ARDL cointegration test	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Zinazohusiana	5	5
Muhtasari	The Fourier ARDL bounds test augments the Pesaran-Shin-Smith cointegration framework with trigonometric (Fourier) terms that capture gradual, smooth structural breaks in the data-generating process. It tests for a long-run level relationship between variables without requiring the researcher to specify the number, timing, or form of structural breaks in advance.	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.