Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals

We investigate the non-ergodic properties of blinking nano-crystals using a stochastic approach. We calculate the distribution functions of the time averaged intensity correlation function and show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe non-ergodicity in systems stochastically modeled using the Levy walk framework for anomalous diffusion, for example certain types of chaotic dynamics, currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated

Estimation for a class of generalized state-space time series models

State-space models with exponential and conjugate exponential family densities are introduced. Examples include Poisson-Gamma, Binomial-Beta, Gamma-Gamma and Normal-Normal processes. Maximum likelihood and quasilikelihood estimators and their properties are discussed. Results from a simulation study for the Poisson-Gamma model are reported.State-space models Exponential families Conjugate exponential families Maximum likelihood estimation Quasilikelihood estimation

Large sample estimation in nonstationary autoregressive processes with multiple observations

The asymptotic distributions of the least-squares estimators of the parameters in autoregressive processes with multiple observations are derived for the two nonstationary cases, viz., (a) the explosive case and (b) the unstable case. It is shown that nonstandard limit distributions are obtained.Autoregression Nonstationary processes Explosive process Unstable process Intraclass correlation Least-squares estimation Asymptotic distributions Nonergodic models

Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors

Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter. Copyright 2005 Blackwell Publishing Ltd.

The asymptotic distribution of the maximum likelihood estimator for a vector time series model with long memory dependence

A vector time series model with long-memory dependence is introduced. It is assumed that, at each time point, the observations are equi-correlated. The model is based on a fractionally differenced autoregressive process (long-memory) adjoined to a Gaussian sequence with constant autocorrelation. The maximum likelihood estimators for the parameters in the model are derived and their asymptotic distributions are obtained.Time series Long-memory dependence Maximum likelihood estimation Asymptotic inference