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Bayesian inference of the fractional Ornstein–Uhlenbeck process under a flow sampling scheme

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  • Theodore Simos

    (University of Ioannina)

  • Mike Tsionas

    (Lancaster University Management School)

Abstract

Using recent developments in econometrics and computational statistics we consider the estimation of the fractional Ornstein–Uhlenbeck process under a flow sampling scheme. To address the problem, we adopt throughout the paper an exact discretization approach. A flow sampling scheme arises, for example, naturally in modelling asset prices in continuous time since the time integral over successive observations defines the observable increments of asset log-prices. Exact discretization delivers an ARIMA(1,1,1) model for log-prices with a fractional driving noise. Building on the resulting exact discretization formulae and covariance function, a new Markov Chain Monte Carlo scheme is proposed and apply it to investigate the properties of both the time and frequency domain likelihoods/posteriors. For the exact discrete model, we adopt a general sampling interval of length h. This allows us to determine the optimal choice of h independent of the sample size. To illustrate the methods, with no ambition to a comprehensive data analysis, we use high frequency stock price data showing the relevance of aggregation over time issues in modelling asset prices.

Suggested Citation

  • Theodore Simos & Mike Tsionas, 2018. "Bayesian inference of the fractional Ornstein–Uhlenbeck process under a flow sampling scheme," Computational Statistics, Springer, vol. 33(4), pages 1687-1713, December.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:4:d:10.1007_s00180-018-0799-6
    DOI: 10.1007/s00180-018-0799-6
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