Parameter estimation for a discrete time model driven by fractional Poisson process

Abstract

In this article, we study the parametric problem of estimating the coefficient for a discrete time model driven by a fractional Poisson noise, when high-frequency observations are given. We consider weighted least squares and maximum likelihood estimators. Thus, asymptotic behavior of the estimators is proved and a simulation study is shown to illustrate our results.

Keywords:

• Fractional Poisson process
• long memory
• weighted least square estimator
• maximum likelihood estimator

2010 AMS CLASSIFICATION NUMBERS:

• 62M09
• 62F10
• 62F12

Additional information

Funding

This research was partially supported by REDES 150038, MEC 80190045, MATHAMSUD 18-MATH-07 SaSMoTiDep Project and MATHAMSUD 16-MATH-03 SIDRE Project. H.A. was partially supported by Proyecto Fondecyt PostDoctorado, Chile 3190465, N.B. was partially supported by FONDECYT Grant 1201898, T.R. was partially supported by Beca CONICYT-PFCHA/Doctorado Nacional/2018-21180298, S.T. was partially supported by FONDECYT Grant 1171335.