Trending time-varying coefficient market models

In this paper we study time-varying coefficient (beta coefficient) models with a time trend function to characterize the nonlinear, non-stationary and trending phenomenon in time series and to explain the behavior of asset returns. The general local polynomial method is developed to estimate the time trend and coefficient functions. More importantly, a graphical tool, the plot of the <italic>k</italic>th-order derivative of the parameter versus time, is proposed to select the proper order of the local polynomial so that the best estimate can be obtained. Finally, we conduct Monte Carlo experiments and a real data analysis to examine the finite sample performance of the proposed modeling procedure and compare it with the Nadaraya--Watson method as well as the local linear method.