Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

This paper discusses nonparametric kernel regression with the regressor being a d-dimensional beta-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate root n(T)h(d), where n(T) is the number of regenerations for a beta-null recurrent process and the limiting distribution (with proper normalization) is normal. Furthermore, we show that the two-step estimator for the volatility function is consistent. The finite sample performance of the estimate is quite reasonable when the leave-one-out cross validation method is used for bandwidth selection. We apply the proposed method to study the relationship of Federal funds rate with 3-month and 5-year T-bill rates and discover the existence of nonlinearity of the relationship. Furthermore, the in-sample and out-of-sample performance of the nonparametric model is far better than the linear model.