Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Traditional time series models often struggle with non-Gaussian marginal distributions.
• Analysts are most familiar with marginal distributions and internal dynamics of time series.
• Existing models may lack flexibility for extensions like changing volatility.

Purpose of the Study:

• To develop a flexible class of Bayesian copula models for stationary time series.
• To integrate nonparametric Bayesian marginal distributions with normal-theory time series dynamics.
• To create models that offer improved fit and predictive performance over Gaussian competitors.

Main Methods:

• Utilizing nonparametric Bayesian prior distributions for marginal distributions.
• Employing a cdf-inverse cdf transformation for broad support of marginal distributions.
• Combining marginal distributions with normal-theory autoregressive dynamics to form copula transformed autoregressive models.
• Modifying the basic model with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) component for volatility analysis.

Main Results:

• The proposed Bayesian copula models successfully recover non-Gaussian marginal distributions.
• A GARCH modification of the models was applied to stock index return series.
• These models demonstrated superior fit and enhanced short-range and long-range predictions compared to Gaussian models.
• The models showed coherence in time scale adjustments and compatibility with extensions.

Conclusions:

• The developed Bayesian copula models provide a powerful and flexible framework for time series analysis.
• These models offer significant advantages over traditional Gaussian competitors in terms of fit and prediction.
• The framework is extensible to diverse areas including continuous time, spatial, and non-stationary models.