This study investigates asset returns within the Iraq Stock Exchange by employing both the Fama-MacBeth regression model and the Fama-French three-factor model. The research involves the estimation of cross-sectional regressions wherein model parameters are subject to temporal variation, and the independent variables function as proxies. The dataset comprises information from the first quarter of 2010 to the first quarter of 2024, encompassing 22 publicly listed companies across six industrial sectors. The study explores methodological advancements through the application of the Single Index Model (SIM) and Kernel Weighted Regression (KWR) in both time series and cross-sectional analyses. The SIM outperformed the KWR approach in estimating time-varying beta coefficients, yielding a mean Root Mean Squared Error (RMSE) of 0.14316. Furthermore, the integrated KWR-SIM methodology achieved the lowest Adjusted Root Mean Squared Error (ARMSE) value of 0.08152 when modelling the association between risk factors and asset returns within the cross-sectional analytical framework. Statistical tests for significance produced heterogeneous responses of the returns on assets in the Iraqi financial market to the Fama-French posited economic variables. The estimated coefficients for the betas showed significant oscillations for all assets, confirming changes in economic conditions. The results add to our knowledge of the risk-reward relationship in the context of emerging markets and provide methodological insights into financial asset pricing. The evidence indicates that the KWR-SIM method has better capabilities for model fitting
