Adaptive estimation of heteroskedastic functional-coefficient regressions with an application to fiscal policy evaluation on asset markets

This article studies the adaptive estimation of the heteroskedastic functional-coefficient regressions. The motivation for such a theoretical study originates from the empirical analysis of Jansen et al., where the role of fiscal policy on the U.S. asset markets (treasury bonds) is evaluated via the functional-coefficient model. It is found that this model is subject to time-varying heteroskedasticity. As a result, the local least square (LLS) estimator suffers from efficiency loss. To overcome this problem, we propose an adaptive LLS (ALLS) estimator, which can adapt to heteroskedasticity of unknown form asymptotically. Simulation studies confirm that the ALLS estimator can achieve significant efficiency gain in finite samples, compared to the LLS estimator. Real data analysis reveals that the heteroskedastic functional-coefficient model provides adequate fit and better out-of-sample forecasting.