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Abstract:
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We propose a class of nonparametric Bayesian models for analyzing stationary time series data using a copula approach, which retains many desirable properties of classic time series models while allowing the innovation distributions to be non-Gaussian. Our models separate estimating the marginal (limiting) distribution of a time series from modeling the internal dynamics of the series. They provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. They are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.
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