Construction and Visualization of Confidence Sets for Frequentist Distributional Forecasts

ABSTRACT

The focus of this article is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use animated graphics to visualize the impact of parameter uncertainty on the location, dispersion, and shape of the distribution. The confidence sets are derived via the inversion of a Wald test, and the ellipsoid that defines the boundary of the set computed numerically. A wide range of linear and nonlinear time series models—encompassing long memory, state space, and mixture specifications—is used to demonstrate the procedure, based on artificially generated data. An empirical example in which distributional forecasts of both financial returns and its stochastic volatility are produced is then used to illustrate the practical importance of accommodating sampling variation in the manner proposed.

KEYWORDS:

• Animated graphics
• Confidence regions
• Heterogeneous autoregressive model
• Probabilistic forecasts
• Realized volatility
• Time series models

Acknowledgments

The authors thank the editor, an associate editor, and two anonymous referees for very constructive comments on earlier drafts of the article.

Funding

This research has been supported by Australian Research Council (ARC) Discovery Grants DP120102344 and DP150101728.