The mode functional is not elicitable

Heinrich, Claudio

doi:10.1093/biomet/ast048

Cited by 37 publications

(46 citation statements)

References 3 publications

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“…Mode regression has received some attention in the recent literature (see, e.g., Silva, 2012 andKemp et al, 2019), however tests for mode forecast rationality similar to those available for the mean and median (e.g., Mincer andZarnowitz, 1969 andGaglianone et al, 2011) are lacking. Direct analogs of existing tests are infeasible because the mode is not elicitable (Heinrich, 2014). We introduce the concept of asymptotic elicitability and show it applies to the mode by considering a generalized modal midpoint with asymptotically vanishing length.…”

Section: Resultsmentioning

confidence: 99%

“…In contrast to the mean and the median, rationality tests for mode forecasts are more challenging to consider. The underlying reason is that there do not exist identification functions for the mode for absolutely continuous distributions (Heinrich, 2014;Dearborn and Frongillo, 2019). For our discussion below, we make the following distinction in the notion of unimodality.…”

Section: The Mode Functionalmentioning

confidence: 99%

“…2 Rationality tests for mean forecasts go back to at least Mincer and Zarnowitz (1969), see Elliott and Timmermann (2016) for a recent survey, while rationality tests for quantile forecasts (nesting median forecasts as a special case) are considered in Christoffersen (1998) and Gaglianone et al (2011). A critical impediment to similar tests for mode forecasts is that the mode is not an "elicitable functional" (Heinrich, 2014), meaning that it cannot be obtained as the solution to an expected loss minimization problem. 3 We obtain a test for mode forecast rationality by first proposing novel results on the asymptotic elicitability of the mode.…”

Section: Introductionmentioning

confidence: 99%

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Testing Forecast Rationality for Measures of Central Tendency

2019

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Rational respondents to economic surveys may report as a point forecast any measure of the central tendency of their (possibly latent) predictive distribution, for example the mean, median, mode, or any convex combination thereof. We propose tests of forecast rationality when the measure of central tendency used by the respondent is unknown. These tests require us to overcome an identification problem when the measures of central tendency are equal or in a local neighborhood of each other, as is the case for (exactly or nearly) symmetric and unimodal distributions. As a building block, we also present novel tests for the rationality of mode forecasts. We apply our tests to survey forecasts of individual income, Greenbook forecasts of U.S. GDP, and random walk forecasts for exchange rates. We find that the Greenbook and random walk forecasts are best rationalized as mean, or near-mean forecasts, while the income survey forecasts are best rationalized as mode forecasts.

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Section: Resultsmentioning

confidence: 99%

Section: The Mode Functionalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Testing Forecast Rationality for Measures of Central Tendency

2019

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“…However, any max-functional has convex level sets by definition. So this approach is not feasible, as in the case of the mode functional (Heinrich, 2014). Instead, we employ the following new criterion.…”

Section: The Elicitation Complexity Of Max-functionalsmentioning

confidence: 99%

Why scoring functions cannot assess tail properties

Brehmer¹,

Strokorb²

2019

Electron. J. Statist.

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Motivated by the growing interest in sound forecast evaluation techniques with an emphasis on distribution tails rather than average behaviour, we investigate a fundamental question arising in this context: Can statistical features of distribution tails be elicitable, i.e. be the unique minimizer of an expected score? We demonstrate that expected scores are not suitable to distinguish genuine tail properties in a very strong sense. Specifically, we introduce the class of max-functionals, which contains key characteristics from extreme value theory, for instance the extreme value index. We show that its members fail to be elicitable and that their elicitation complexity is in fact infinite under mild regularity assumptions. Further we prove that, even if the information of a max-functional is reported via the entire distribution function, a proper scoring rule cannot separate max-functional values. These findings highlight the caution needed in forecast evaluation and statistical inference if relevant information is encoded by such functionals.

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“…Many important statistical functionals such as the variance, the ES, the minimum, the maximum and the mode are not elicitable, i.e. no strictly consistent loss functions exist (Gneiting, 2011;Heinrich, 2014;. This deficiency calls for generalized approaches in many academic disciplines.…”

Section: Theorymentioning

confidence: 99%

Forecast Encompassing Tests for the Expected Shortfall

Dimitriadis

Schnaitmann

2019

SSRN Journal

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We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk measure for the international banking regulation. We utilize joint loss functions for the pair ES and Value at Risk to set up three ES encompassing test variants. The tests are built on misspecification robust asymptotic theory and we verify the finite sample properties of the tests in an extensive simulation study. We use the encompassing tests to illustrate the potential of forecast combination methods for different financial assets.

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The mode functional is not elicitable

Cited by 37 publications

References 3 publications

Testing Forecast Rationality for Measures of Central Tendency

Testing Forecast Rationality for Measures of Central Tendency

Why scoring functions cannot assess tail properties

Forecast Encompassing Tests for the Expected Shortfall

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