 On the Comparison of Interval ForecastsRoss Askanazi, Francis Diebold, Frank Schorfheide and Minchul Shin Journal of Time Series Analysis, 2018, vol. 39, issue 6, 953-965 Abstract: We explore interval forecast comparison when the nominal confidence level is specified, but the quantiles on which intervals are based are not specified. It turns out that the problem is difficult, and perhaps unsolvable. We first consider a situation where intervals meet the Christoffersen conditions (in particular, where they are correctly calibrated), in which case the common prescription, which we rationalize and explore, is to prefer the interval of shortest length. We then allow for mis‐calibrated intervals, in which case there is a calibration‐length tradeoff. We propose two natural conditions that interval forecast loss functions should meet in such environments, and we show that a variety of popular approaches to interval forecast comparison fail them. Our negative results strengthen the case for abandoning interval forecasts in favor of density forecasts: Density forecasts not only provide richer information, but also can be readily compared using known proper scoring rules like the log predictive score, whereas interval forecasts cannot. Date: 2018 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:39:y:2018:i:6:p:953-965 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Time Series Analysis is currently edited by M.B. Priestley More articles in Journal of Time Series Analysis from Wiley Blackwell |
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