Linganisha mbinu

	Mchanganuo wa Kiasi-Patanishi	Njia ya Wakati wa Regression ya Kiasi	ARDL ya Kiasi
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2012	2004	2006
Mwanzilishi	Oliver Linton and Yoon-Jin Whang	Roger Koenker and colleagues	Roger Koenker and Zhijie Xiao
Aina	Correlation measure	Distribution regression	Conditional distribution model
Chanzo asilia	Linton, O., & Whang, Y. J. (2012). Quantile comparisons of time series data. Journal of Econometrics, 170(2), 242-257.	Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74-89.	Koenker, R., & Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association, 101(475), 980-990.
Majina mbadala	—	GMM quantile regression	Quantile ARDL
Zinazohusiana	3	3	3
Muhtasari	The cross-quantilogram extends the cross-correlogram concept to quantile pairs of two time series, measuring dependence at different quantile levels. Introduced by Linton and Whang (2012), it captures how shocks at specific quantile levels in one series relate to movements in another, enabling asymmetric dependence analysis. This approach is particularly valuable when downside and upside risk correlations differ materially.	Method of Moments Quantile Regression combines moment-based estimation (GMM) with quantile regression to estimate distribution parameters while handling endogeneity, panel structure, and dynamic relationships. Introduced by Koenker (2004) and developed by Machado and Mata (2005), it enables distributional analysis (not just mean regression) in complex settings like dynamic panels and instrumental-variable contexts. This approach is powerful for understanding heterogeneity in treatment effects and policy impacts.	QARDL (Quantile Autoregressive Distributed Lag) combines quantile regression with ARDL modeling to estimate conditional relationships at different points of the distribution, revealing heterogeneous short-run and long-run effects. Introduced by Koenker and Xiao (2006) and refined by Cho et al. (2015), it captures how the effect of explanatory variables on outcomes varies across quantiles, essential for understanding tail behavior and distributional impacts rather than just mean effects.