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Estimating doubly stochastic Poisson process with affine intensities by Kalman filter

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  • Alan Genaro
  • Adilson Simonis

Abstract

This paper proposes a Kalman filter formulation for parameter estimation of doubly stochastic Poisson processes (DSPP) with stochastic affine intensities. To achieve this aim, an analytical expression for the probability distribution functions of the corresponding DSPP for any intensity from the class of affine diffusions is obtained. More detailed results are provided for one- and two-factor Feller and Ornstein–Uhlenbeck diffusions. A Monte Carlo study indicates that the proposed method is a reliable procedure for moderate sample sizes. An empirical analysis of one- and two-factor Feller and Ornstein–Uhlenbeck models is carried out using high frequency transaction data. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Alan Genaro & Adilson Simonis, 2015. "Estimating doubly stochastic Poisson process with affine intensities by Kalman filter," Statistical Papers, Springer, vol. 56(3), pages 723-748, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:723-748
    DOI: 10.1007/s00362-014-0606-6
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    1. Paula R. Bouzas & Nuria Ruiz-Fuentes & Carmen Montes-Gijón & Juan Eloy Ruiz-Castro, 2021. "Forecasting counting and time statistics of compound Cox processes: a focus on intensity phase type process, deletions and simultaneous events," Statistical Papers, Springer, vol. 62(1), pages 235-265, February.

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