On Berry--Esseen bounds for non-instantaneous filters of linear processes

Let $X_n=\sum_{i=1}^{\infty}a_i\epsilon_{n-i}$, where the $\epsilon_i$ are i.i.d. with mean 0 and at least finite second moment, and the $a_i$ are assumed to satisfy $|a_i|=O(i^{-\beta})$ with $\beta >1/2$. When $1/2<\beta<1$, $X_n$ is usually called a long-range dependent or long-memory process. For a certain class of Borel functions $K(x_1,...,x_{d+1})$, $d\ge0$, from ${\mathcal{R}}^{d+1}$ to $\mathcal{R}$, which includes indicator functions and polynomials, the stationary sequence $K(X_n,X_{n+1},...,X_{n+d})$ is considered. By developing a finite orthogonal expansion of $K(X_n,...,X_{n+d})$, the Berry--Esseen type bounds for the normalized sum $Q_N/\sqrt{N},Q_N=\sum_{n=1}^N(K(X_ n,...,X_{n+d})-\mathrm{E}K(X_n,...,X_{n+d}))$ are obtained when $Q_N/\sqrt{N}$ obeys the central limit theorem with positive limiting variance.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ112 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Comparison of Nonlinear Phase Noise and Intrachannel Four-Wave-Mixing for RZ-DPSK Signals in Dispersive Transmission Systems

Self-phase modulation induced nonlinear phase noise is reduced with the increase of fiber dispersion but intrachannel four-wave-mixing (IFWM) is increased with dispersion. Both degrading DPSK signals, the standard deviation of nonlinear phase noise induced differential phase is about three times that from IFWM even in highly dispersive transmission systems.Comment: 3 pages, 2 figure

Polyelectrolyte Adsorption on Charged Substrate

The behavior of a polyelectrolyte adsorbed on a charged substrate of high-dielectric constant is studied by both Monte-Carlo simulation and analytical methods. It is found that in a low enough ionic strength medium, the adsorption transition is first-order where the substrate surface charge still keeps repulsive. The monomer density at the adsorbed surface is identified as the order parameter. It follows a linear relation with substrate surface charge density because of the electrostatic boundary condition at the charged surface. During the transition, the adsorption layer thickness remains finite. A new scaling law for the layer thickness is derived and verified by simulation.Comment: Proceedings of the 3rd Symposium on Slow Dynamics in Complex Systems, 3-8 November 2003, Sendai, Japa

Purchasing Power Parity and Country Characteristics: Evidence from Time Series Analysis

This paper investigates the relationships between country characteristics and the validity of PPP. We use three alternative time series methods to test for the stationarity of real exchange rates for each of the 72 countries over the period from 1976 to 2005. Our result shows that the evidence of PPP exhibits geographic difference. It is most likely to find stationary real exchange rates for European countries, whereas it is least likely to obtain the result of supporting PPP for Asian countries. We then use a probit regression model to examine if county characteristics are related to the validity of PPP. The probit regression result reveals that the validity of PPP decreases with inflation rate and increases with nominal exchange rate volatility.Purchasing power parity, Country characteristics, Unit root tests

Simultaneous Amplitude and Phase Measurement for Periodic Optical Signals Using Time-Resolved Optical Filtering

Time-resolved optical filtering (TROF) measures the spectrogram or sonogram by a fast photodiode followed a tunable narrowband optical filter. For periodic signal and to match the sonogram, numerical TROF algorithm is used to find the original complex electric field or equivalently both the amplitude and phase. For phase-modulated optical signals, the TROF algorithm is initiated using the craters and ridges of the sonogram.Comment: 10 pages, 5 figure