| The predictive regression model has been studied and widely applied in economics and finance in the last two decades, while several difficulties associated with the classical predictive models have not been solved out appropriately. In this dissertation, my aim is to look for solutions to these difficulties for both linear and nonlinear predictive regression models.;The "endogeneity" and high persistency of the predictive variables are the two main problems embedded in the linear predictive models. To remove the "endogeneity", the linear projection is commonly applied to deal with the two innovations in the predictive model and the model for regressors, and then the ordinary least square method is adopted to estimate the coefficients. The asymptotic distributions of these estimates are established assuming alpha-mixing innovations and these asymptotic results show that convergence rates for different coefficients are different due to the highly persistent nature of the state variable. In addition, we show that if there is a drift in the autoregressive model for the state variable, the asymptotic distribution of the predicting coefficient would be changed with a faster convergence rate. In order to check the significance of the unknown coefficients, the Monte Carlo simulation method is used to find the appropriate critical values.;In order to deal with the possible instability of the predictability associated to the linear predictive model, I propose a time-varying coefficient predictive model, which also takes account of the "endogeneity" and persistent state variables such as nearly integrated or integrated processes. The local linear approach is used to estimate the time-varying coefficient functions, and the asymptotic distributions of these estimates are developed for alpha-mixing innovations. Again, the difference between the asymptotic distributions of the estimated predicting coefficient under the conditions with or without a drift in the AR model is discussed. Based on the asymptotic theory, it can be shown that the orders iv of the bandwidths used to estimate the intercept and slope functions are different, which implies that a two stage estimation procedure should be considered in order to obtain the optimal estimations for all coefficients. In addition, an L2 type of statistic is proposed to check the stability of the coefficient vector, and the asymptotic distributions of the test statistic under the null and alternative hypotheses are developed respectively.;For both models, finite sample results are investigated using Monte Carlo simulation studies in order to show the usefulness of the estimation method and the test statistics. Also the empirical applications to the predictability of CRSP monthly returns are also implemented to illustrate our proposed models and methods. |
