Central limit theorem for asymmetric kernel functionals

Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.