Nonparametric Regression Models for Nonstationary Variables with Applications
  in Economics and Finance

  Zongwu Cai
  E-mail: zcai@uncc.edu
  Department of Mathematics & Statistics and Department of Economics
  University of North Carolina at Charlotte, Charlotte, NC 28223, USA
  and
  Wang Yanan Institute for Studies in Economics, Xiamen University, China


 ABSTRACT:
 In this talk, I will talk about how to use a nonparametric regression model to do forecasting
 for nonstationary economic and financial data, for example, to forecast the inflation rate
 using the velocity variable in economics and to test predictability efficiency in stock returns
 using the log dividend-price ratio and/or the log earnings-price ratio and/or the three-month
 T-bill and/or the long-short yield spread.
 A local linear approach is developed to estimate the unknown functionals.
 The consistency and asymptotic normality of the proposed estimators are obtained.
 Our asymptotic results show that the asymptotic bias is same for all estimators of
 coefficient functions but the convergence rates are totally different for stationary
 and nonstationary covariates. The convergence rate for the estimators of the coefficient
 functions for nonstationary covariates is faster than that for stationary covariates
 with a factor of $n^{-1/2}$. This finding seems new and it leads to a two-stage approach
 to improve the estimation efficiency.
 When the coefficient function is a function of nonstationary variable, our new findings are
 that the asymptotic bias term is the same as that for stationary case but the convergence
 rate is different and further, the asymptotic distribution is not a normal but a mixed
 normal associated with the local time of a standard Brownian motion.
 Moreover, the asymptotic behaviors at boundaries are investigated.
 The proposed methodology is illustrated with an economic time series, which exhibits
 nonlinear and nonstationary behavior.
 This is a join work with Qi Li, Department of Economics, Texas A&M University and
 Peter M. Robinson, Department of Economics, London School of Economics.