Shannon entropy estimation for linear processes

Abstract

In this paper, we estimate the Shannon entropy $S(f) = -\E[ \log (f(x))]$ of a one-sided linear process with probability density function $f(x)$. We employ the integral estimator $S_n(f)$, which utilizes the standard kernel density estimator $f_n(x)$ of $f(x)$. We show that $S_n(f)$ converges to $S(f)$ almost surely and in ${Ł}^2$ under reasonable conditions.

14 pages, accepted by Journal of Risk and Financial Management