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Identifying Restrictions for Finite Parameter Continuous Time Models with Discrete Time Data

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  • Jason R. Blevins

    (Department of Economics, Ohio State University)

Abstract

When a continuous time model is sampled only at equally spaced intervals, a priori restrictions on the parameters can provide natural identifying restrictions which serve to rule out otherwise observationally equivalent parameter values. Specifically, we consider identification of the parameter matrix in a linear system of first-order stochastic differential equations, a setting which is general enough to include many common continuous time models in economics and finance. We derive a new characterization of the identification problem under a fully general class of linear restrictions on the parameter matrix and establish conditions under which only floor(n/2) restrictions are sufficient for identification when only the discrete time process is observable. Restrictions of the required kind are typically implied by economic theory and include zero restrictions that arise when some variables are excluded from an equation. We also consider identification of the intensity matrix of a discretely-sampled finite Markov jump processes, a related special case where we show that only floor((n-1)/2) restrictions are required. We demonstrate our results by applying them to two example models from economics and finance: a continuous time regression model with three equations and a continuous-time model of credit rating dynamics.

Suggested Citation

  • Jason R. Blevins, 2013. "Identifying Restrictions for Finite Parameter Continuous Time Models with Discrete Time Data," Working Papers 13-01, Ohio State University, Department of Economics.
  • Handle: RePEc:osu:osuewp:13-01
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    File URL: http://www.econ.ohio-state.edu/pdf/blevins/wp13-01.pdf
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    Cited by:

    1. Nail Kashaev & Natalia Lazzati, 2019. "Peer Effects in Random Consideration Sets," Papers 1904.06742, arXiv.org, revised May 2021.
    2. Vicky Fasen-Hartmann & Celeste Mayer, 2022. "Whittle estimation for continuous-time stationary state space models with finite second moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 233-270, April.
    3. 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.
    4. Hong, Han & Li, Weiming & Wang, Boyu, 2015. "Estimation of dynamic discrete models from time aggregated data," Journal of Econometrics, Elsevier, vol. 188(2), pages 435-446.

    More about this item

    Keywords

    stochastic differential equations; identification; continuous time regression; Markov jump process; matrix exponential; matrix logarithm;
    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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