Efficient estimation of a semiparametric partially linear smooth coefficient model

In this dissertation I propose a general series method to estimate the semiparametric partially linear smooth coefficient model. The consistency and $n$-normality property of the estimated parameters of the partially linear part are established and furthermore it attains the semiparametric efficiency bound when the error is conditional homoskedastic. The convergence rates of the estimators of the smooth coefficient functions are also derived and a simulation is conducted to make the results more concrete.; The application of this model is illustrated by the case of inflation rate forecasting using the unemployment rate and the industry capacity utilization rate. Forecasting efficiency is compared using the simple autoregressive model, the smooth coefficient model, and a semiparametric partially linear smooth coefficient model. Specification tests are also performed.; Another application in this dissertation is to show that one can better forecast inflation using the past information of money growth by allowing for potentially complicated nonlinearities in the relationship between money growth and inflation. Many nonparametric and semiparametric models have been used to compare the forecasting efficiency with the parametric VAR approach.