Michael Stanley Smith
arXiv 10 Sep 2021 · Statistics — Methodology
arXiv:2109.04718 · PDF · Extracted main text
Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and regression copulas. The common auxiliary representation of implicit copulas is outlined, and how this makes them both scalable and tractable for statistical modeling. Issues such as parameter identification, extended likelihoods for discrete or mixed data, parsimony in high dimensions, and simulation from the copula model are considered. Bayesian approaches to estimate the copula parameters, and predict from an implicit copula model, are outlined. Particular attention is given to implicit copula processes constructed from time series and regression models, which is at the forefront of current research. Two econometric applications -- one from macroeconomic time series and the other from financial asset pricing -- illustrate the advantages of implicit copula models.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Smith, M.S (2015) Copula modelling of dependence in multivariate time series self | 1.000 | 6 | 3 | 100% |
| 2 | Loaiza-Maya, R., Smith, M.S (2019) Variational Bayes estimation of discrete-margined copula models with application to time series self | 1.000 | 5 | 4 | 100% |
| 3 | Loaiza-Maya, R., Smith, M.S., Maneesoonthorn, W (2018) Time series copulas for heteroskedastic data self | 1.000 | 5 | 3 | 100% |
| 4 | Smith, M.S., Gan, Q., Kohn, R.J (2012) Modelling dependence using skew t copulas: Bayesian inference and applications self | 1.000 | 5 | 3 | 100% |
| 5 | Smith, M.S., Maneesoonthorn, W (2018) Inversion copulas from nonlinear state space models with an application to inflation forecasting self | 0.941 | 6 | 5 | 83% |
| 6 | McNeil, A.J., Frey, R., Embrechts, R (2005) Quantitative Risk Management: Concepts, Techniques and Tools | 0.928 | 4 | 3 | 100% |
| 7 | Danaher, P.J., Smith, M.S (2011) Modeling multivariate distributions using copulas: Applications in marketing self | 0.928 | 4 | 3 | 100% |
| 8 | Nelsen, R.B (2006) An Introduction to Copulas | 0.928 | 4 | 3 | 100% |
| 9 | Pitt, M., Chan, D., Kohn, R (2006) Efficient Bayesian inference for Gaussian copula regression models | 0.928 | 4 | 3 | 100% |
| 10 | Klein, N., Smith, M.S (2019) Implicit copulas from Bayesian regularized regression smoothers self | 0.874 | 7 | 2 | 100% |
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