Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations

Reiichiro Kawai, Hiroki Masuda

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)

    Abstract

    We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in (0, 1) and the other with index in (1, 2). We discuss simulation techniques for those three random elements. With the exact transition law and proposed simulation techniques, sample paths simulation proves significantly more efficient, relative to the known approximative technique based on infinite shot noise series representation of tempered stable Lévy processes.

    Original languageEnglish
    Pages (from-to)125-139
    Number of pages15
    JournalCommunications in Statistics: Simulation and Computation
    Volume41
    Issue number1
    DOIs
    Publication statusPublished - Jan 2012

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Modelling and Simulation

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