Ruben Loaiza-Maya, Michael Stanley Smith
arXiv 26 Dec 2017 · Statistics — Methodology · publishedJournal of Computational and Graphical Statistics (2019) · 14 citations (OpenAlex)
arXiv:1712.09150 · PDF · DOI · OpenAlex · Extracted main text
We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a feature of most ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. Using six example series, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods.
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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 | Ong, V. M.-H., Nott, D. J., and Smith, M. S (2017) Gaussian variational approximation with a factor covariance structure self | 1.000 | 8 | 5 | 100% |
| 2 | Smith, M. S (2015) Copula modelling of dependence in multivariate time series self | 1.000 | 8 | 3 | 100% |
| 3 | Smith, M. and Khaled, M (2012) Estimation of Copula Models With Discrete Margins via Bayesian Data Augmentation self | 1.000 | 7 | 4 | 100% |
| 4 | Loaiza-Maya, R., Smith, M. S., and Maneesoonthorn, W (2018) Time Series Copulas for Heteroskedastic Data self | 1.000 | 6 | 4 | 100% |
| 5 | Beare, B. K. and Seo, J (2015) Vine Copula Specifications for Stationary Multivariate Markov Chains | 0.928 | 4 | 3 | 100% |
| 6 | Tran, M.-N., Nott, D. J., and Kohn, R (2017) Variational Bayes With Intractable Likelihood | 0.843 | 3 | 3 | 100% |
| 7 | Gunawan, D., Tran, M.-N., Suzuki, K., Dick, J., and Kohn, R (2016) Computationally Efficient Bayesian Estimation of High Dimensional Copulas with Discrete and Mixed Margins | 0.737 | 3 | 2 | 100% |
| 8 | Aas, K., Czado, C., Frigessi, A., and Bakken, H (2009) Pair-copula constructions of multiple dependence | 0.644 | 2 | 2 | 100% |
| 9 | Hui, F. K., Warton, D. I., Ormerod, J. T., Haapaniemi, V., and Taski… (2017) Variational Approximations for Generalized Linear Latent Variable Models | 0.644 | 2 | 2 | 100% |
| 10 | Tan, L. S. L. and Nott, D. J (2017) Gaussian variational approximation with sparse precision matrices | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 52 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Implicit Copulas: An Overview | 1.000 | 5 | 4 |
| 2 | myblue Cutting Feedback in Misspecified Copula Models | 0.737 | 3 | 2 |
| 3 | Fast and Accurate Variational Inference for Models with Many Latent Variables | 0.405 | 1 | 1 |
| 4 | myblue Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns | 0.405 | 1 | 1 |