Nonparametric estimation of kernel functions of Brownian semi-stationary processes with an application to electricity markets

This paper considers nonparametric estimation of Brownian
semi-stationary (BSS) processes. We establish fully nonparametric identification of the so-called kernel function through the autocovariance function of our the process of interest. This identification result allows us to propose a new nonparametric series-based estimator of the kernel function by matching t
he sample autocovariance function with the model-implied. We investigate finite-sample properties of the proposed estimator through a simulation study, and apply it to the study of spot price data from electricity markets.