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Construction and Visualization of Confidence Sets for Frequentist Distributional Forecasts
Authors:David Harris  Gael M Martin  Indeewara Perera  D S Poskitt
Institution:1. Department of Economics, The University of Melbourne, Melbourne, Australia;2. Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia;3. Department of Economics, The University of Sheffield, Sheffield, UK
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
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