Journal
JOURNAL OF BUSINESS & ECONOMIC STATISTICS
Volume 33, Issue 2, Pages 270-281Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/07350015.2014.948175
Keywords
Moment test; Density forecast evaluation; Normality test; Probability integral transformation
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The evaluation of multi-step-ahead density forecasts is complicated by the serial correlation of the corresponding probability integral transforms. In the literature, three testing approaches can be found that take this problem into account. However, these approaches rely on data-dependent critical values, ignore important information and, therefore lack power, or suffer from size distortions even asymptotically. This article proposes a new testing approach based on raw moments. It is extremely easy to implement, uses standard critical values, can include all moments regarded as important, and has correct asymptotic size. It is found to have good size and power properties in finite samples if it is based on the (standardized) probability integral transforms.
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