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The exact discretisation of CARMA models with applications in finance

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  • Thornton, Michael A.
  • Chambers, Marcus J.

Abstract

The problem of estimating a continuous time model using discretely observed data is common in empirical finance. This paper uses recently developed methods of deriving the exact discrete representation for a continuous time ARMA (autoregressive moving average) system of order p, q to consider three popular models in finance. Our results for two benchmark term structure models show that higher order ARMA processes provide a significantly better fit than standard Ornstein–Uhlenbeck processes. We then explore present value models linking stock prices and dividends in the presence of cointegration. Our methods enable us to take account of the fact that the two variables are observed in fundamentally different ways by explicitly modelling the data as mixed stock–flow type, which we then compare with the (more common, but incorrect) treatment of dividends as a stock variable.

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  • Thornton, Michael A. & Chambers, Marcus J., 2016. "The exact discretisation of CARMA models with applications in finance," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 739-761.
    • Handle: RePEc:eee:empfin:v:38:y:2016:i:pb:p:739-761
    DOI: 10.1016/j.jempfin.2016.03.006
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    Cited by:

    1. Thornton, Michael A. & Chambers, Marcus J., 2017. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 48-65.
    2. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.

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    More about this item

    Keywords

    Continuous time ARMA process; Discrete time representation; Present value; Term structure;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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