In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economic...

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 Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely...

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 Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely...

For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with the same covariance structure. This class contains both...

Let {Xn, n [greater-or-equal, slanted] 1} be a stationary [rho]-mixing sequence of random variables with EX1 = , EX12+[delta] for some and Var Sn --> [infinity] as n --> [infinity]. This note presents a class of estimators of Var Sn, without assuming any mixing rate.

Asymptotic properties of a non-linear smoothing algorithm are analyzed. It is shown that under appropriate conditions the output of the algorithm is absolutely regular and that partial sums are asymptotically normal.