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Asymptotic Likelihood Based Inference for Co‐integrated Homogenous Gaussian Diffusions

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  • Mathieu Kessler
  • Anders Rahbek

Abstract

In this paper we consider inference for a multivariate Gaussian homogenous diffusion which is co‐integrated, i.e. admits a representation in terms of stable relations (ergodic diffusions) plus Brownian motions. We show that inference on co‐integration rank (the number of stable relations) in continuous time can be based on existing asymptotic distributions from discrete time co‐integration analysis. Likewise the asymptotic distributions of the co‐integration parameters are shown to be mixed Gaussian. Special attention is given to the parametrization of the drift terms. It is shown that the asymptotic distribution of the co‐integration rank test statistic does not depend on the level of the process as a result of the chosen parametrization.

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  • Mathieu Kessler & Anders Rahbek, 2001. "Asymptotic Likelihood Based Inference for Co‐integrated Homogenous Gaussian Diffusions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 455-470, September.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:3:p:455-470
    DOI: 10.1111/1467-9469.00248
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    Cited by:

    1. Gustavo Fruet Dias & Marcelo Fernandes & Cristina M. Scherrer, 2016. "Component shares in continuous time," CREATES Research Papers 2016-25, Department of Economics and Business Economics, Aarhus University.
    2. Felix Pretis, 2015. "Econometric Models of Climate Systems: The Equivalence of Two-Component Energy Balance Models and Cointegrated VARs," Economics Series Working Papers 750, University of Oxford, Department of Economics.
    3. Gustavo Fruet Dias & Karsten Schweiker, 2024. "Integrated Variance Estimation for Assets Traded in Multiple Venues," University of East Anglia School of Economics Working Paper Series 2024-04, School of Economics, University of East Anglia, Norwich, UK..
    4. Pretis, Felix, 2020. "Econometric modelling of climate systems: The equivalence of energy balance models and cointegrated vector autoregressions," Journal of Econometrics, Elsevier, vol. 214(1), pages 256-273.
    5. Bahman Angoshtari, 2016. "On the Market-Neutrality of Optimal Pairs-Trading Strategies," Papers 1608.08268, arXiv.org.
    6. M. Kessler & A. Rahbek, 2004. "Identification and Inference for Multivariate Cointegrated and Ergodic Gaussian Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 137-151, May.
    7. Dias, Gustavo Fruet & Fernandes, Marcelo & Scherrer, Cristina Mabel, 2017. "Improving on daily measures of price discovery," Textos para discussão 444, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    8. Chambers, M.J. & McCrorie, J.R., 2004. "Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems," Discussion Paper 2004-40, Tilburg University, Center for Economic Research.
    9. Kuck, Konstantin & Schweikert, Karsten, 2023. "Price discovery in equity markets: A state-dependent analysis of spot and futures markets," Journal of Banking & Finance, Elsevier, vol. 149(C).

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