Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes (unidimensional andmultidimensional)process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is a...

This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predict...

Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is also discussed. Data from the symbol ...

The gut microbiome is a dynamic system that changes with host development, health, behavior, diet, and microbe-microbe interactions. Prior work on gut microbial time series has largely focused on autoregressive models (e.g. Lotka-Volterra). However, we show that most of the variance in microbial time series is non-autoregressive. In addition, we show how community state-clustering is flawed whe...

A class of nonstationary time series such as locally stationary time series can be approximately modeled by piecewise stationary autoregressive (PSAR) processes. But the number and locations of the piecewise autoregressive segments, as well as the number of nonzero coefficients in each autoregressive process, are unknown. In this talk, by connecting the multiple structural break detection with ...

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares estimator for these coefficients has a normal limit distribution. If none of the parameters equals zero than the typical rate of convergence is n. AMS 2000 s...