Parameter estimation for fractional Poisson processes

Parameter Estimation for Fractional Poisson Processes

The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data with long memory is to make the standard Poisson model more flexible by permitting nonexponential, heavy-tailed distributions of interarrival times and differe...

Parameter estimation for fractional Ornstein-Uhlenbeck processes

We study a least squares estimator b θT for the Ornstein-Uhlenbeck process, dXt = θXtdt+σdB H t , driven by fractional Brownian motion B H with Hurst parameter H ≥ 1 2 . We prove the strong consistence of b θT (the almost surely convergence of b θT to the true parameter θ). We also obtain the rate of this convergence when 1/2 ≤ H < 3/4, applying a central limit theorem for multiple Wiener integ...

Parameter Estimation for Multi-dimensional Filtered Poisson Processes

Estimation of the Hurst parameter in some fractional processes

We propose to estimate the Hurst parameter involved in fractional processes via a method based on the Karhunen-Loève expansion of Gaussian process.We specifically investigate the cases of the Fractional Brownian motion(FBm) and the Fractional Ornstein-Uhlenbeck(FOU) Family. The main tool is the analysis of the residuals of a convenient linear regression model. We numerically compare our results...

Poisson-Lindley INAR(1) Processes: Some Estimation and Forecasting Methods

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...