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Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series

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Document pages: 32 pages

Abstract: We propose a new variational Bayes estimator for high-dimensional copulaswith discrete, or a combination of discrete and continuous, margins. The methodis based on a variational approximation to a tractable augmented posterior, andis faster than previous likelihood-based approaches. We use it to estimatedrawable vine copulas for univariate and multivariate Markov ordinal and mixedtime series. These have dimension $rT$, where $T$ is the number of observationsand $r$ is the number of series, and are difficult to estimate using previousmethods. The vine pair-copulas are carefully selected to allow forheteroskedasticity, which is a feature of most ordinal time series data. Whencombined with flexible margins, the resulting time series models also allow forother common features of ordinal data, such as zero inflation, multiple modesand under- or over-dispersion. Using six example series, we illustrate both theflexibility of the time series copula models, and the efficacy of thevariational Bayes estimator for copulas of up to 792 dimensions and 60parameters. This far exceeds the size and complexity of copula models fordiscrete data that can be estimated using previous methods.

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