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Approximate likelihood with proxy variables for parameter estimation in high-dimensional factor copula models

Author

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  • Pavel Krupskii

    (University of Melbourne)

  • Harry Joe

    (University of British Columbia)

Abstract

Factor copula models involve latent variables that explain much of the dependence in the observed variables. Their log-likelihoods can involve one-dimensional or multi-dimensional integration. For the one-factor copula with weak residual dependence and for the oblique factor copula model, we show that, under some mild assumptions, proxy variables that are unweighted averages computed from the observed variables can be used for the latent variables when the dimension is large. Then alternative log-likelihoods without integrals can be used for parameter estimation. The proxy variables can help to select appropriate linking copulas in some factor copula models and to perform numerically faster maximum likelihood estimation of parameters. Simulation studies show that parameter estimates obtained using the proxy variable approach are close to those obtained using the maximum likelihood approach. The proxy variable approach is used to analyze a financial data set of stock returns in a single sector.

Suggested Citation

  • Pavel Krupskii & Harry Joe, 2022. "Approximate likelihood with proxy variables for parameter estimation in high-dimensional factor copula models," Statistical Papers, Springer, vol. 63(2), pages 543-569, April.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01252-1
    DOI: 10.1007/s00362-021-01252-1
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    References listed on IDEAS

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    1. Pavel Krupskii & Marc G. Genton, 2018. "Linear factor copula models and their properties," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 861-878, December.
    2. Hoang Nguyen & M Concepción Ausín & Pedro Galeano, 2019. "Parallel Bayesian Inference for High-Dimensional Dynamic Factor Copulas," Journal of Financial Econometrics, Oxford University Press, vol. 17(1), pages 118-151.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Dong Hwan Oh & Andrew J. Patton, 2013. "Simulated Method of Moments Estimation for Copula-Based Multivariate Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 689-700, June.
    5. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    6. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    7. Brechmann, Eike C. & Joe, Harry, 2014. "Parsimonious parameterization of correlation matrices using truncated vines and factor analysis," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 233-251.
    8. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    9. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
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