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Abstract
The market model, also known as single factor model or the -representation in Capital Asset Pricing Model (CAPM) context, is a purely statistical model used to explain the behavior of asset returns. In this paper we study time-varying coefficient models with time trend function to characterize non-linear, non-stationary and trending phenomenon in time series. Compared with the Nadaraya-Watson method and the local linear approach, the general local polynomial approach is developed to estimate the time trend and coefficient functions. Bandwidth is selected based on the nonparametric version of the Akaike information criterion (AIC). In our general local polynomial method, we plot the derivatives of the parameters vs. time. These graphs provide a useful way to estimate what local polynomial orders we should use for data analysis. Finally, we conduct some Monte Carlo experiments to examine the finite sample performances of the proposed modeling procedure, and an empirical example is discussed by checking the regression coefficients between individual stocks and S&P 500 index (market portfolio). KEY WORDS: Bandwidth selection; Functional coefficient models; Nadaraya-Watson estimation; Local linear estimate; local polynomial estimate, Nonlinearity; Nonstationarity; Stationarity; Time series errors. ii