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Noncausality in Continuous Time Models

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  • Comte, F.
  • Renault, E.

Abstract

In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.

Suggested Citation

  • Comte, F. & Renault, E., 1996. "Noncausality in Continuous Time Models," Econometric Theory, Cambridge University Press, vol. 12(2), pages 215-256, June.
    • Handle: RePEc:cup:etheor:v:12:y:1996:i:02:p:215-256_00
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    Cited by:

    1. Sauri, Orimar & Veraart, Almut E.D., 2017. "On the class of distributions of subordinated Lévy processes and bases," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 475-496.
    2. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," University of California at Los Angeles, Anderson Graduate School of Management qt9mf223rs, Anderson Graduate School of Management, UCLA.
    3. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO.
    4. Petrović, Ljiljana & Dimitrijević, Sladjana, 2012. "Causality with finite horizon of the past in continuous time," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1219-1223.
    5. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 207-226, November.
    6. McCrorie, J. Roderick & Chambers, Marcus J., 2006. "Granger causality and the sampling of economic processes," Journal of Econometrics, Elsevier, vol. 132(2), pages 311-336, June.
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    8. Magnus, Jan R. & Pijls, Henk G.J. & Sentana, Enrique, 2021. "The Jacobian of the exponential function," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    9. Tata Subba Rao & Granville Tunnicliffe Wilson & Michael Eichler & Rainer Dahlhaus & Johannes Dueck, 2017. "Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 225-242, March.
    10. Cai, Charlie X. & Mobarek, Asma & Zhang, Qi, 2017. "International stock market leadership and its determinants," Journal of Financial Stability, Elsevier, vol. 33(C), pages 150-162.
    11. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    12. 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.
    13. Dragana Valjarević, 2024. "Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation," Mathematics, MDPI, vol. 12(5), pages 1-11, February.

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