On Construction of Higher Order Kernels Using Fourier Transforms and Covariance Functions

In this paper, we show that a suitably chosen covariance function of a continuous time, second order stationary stochastic process can be viewed as a symmetric higher order kernel. This leads to the construction of a higher order kernel by choosing an appropriate covariance function. An optimal choice of the constructed higher order kernel that partially minimizes the mean integrated square error of the kernel density estimator is also discussed.