Higher Moment Constraints for Predictive Density Combination

Pauwels, Laurent L.; Radchenko, Peter; Vasnev, Andrey L.

doi:10.2139/ssrn.3593124

Cited by 5 publications

(3 citation statements)

References 39 publications

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“…Our results con-tribute to the active literature on frequentist estimation of linear predictive combinations via predictive criteria (e.g. Hall and Mitchell, 2007, Ranjan and Gneiting, 2010, Clements and Harvey, 2011, Geweke and Amisano, 2011, Gneiting and Ranjan, 2013, Kapetanios et al, 2015, Opschoor et al, 2017, Ganics, 2018and Pauwels et al, 2020. In particular, our results provide a possible explanation behind the often mixed out-of-sample performance of optimal weighting schemes.…”

Section: Introductionsupporting

confidence: 78%

Optimal probabilistic forecasts: When do they work?

Martin¹,

Loaiza-Maya²,

Frazier³

et al. 2020

Preprint

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Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different scoring rules rewarding distinct aspects of forecast performance. Herein, we reinvestigate the practice of using proper scoring rules to produce probabilistic forecasts that are 'optimal' according to a given score, and assess when their out-of-sample accuracy is superior to alternative forecasts, according to that score. Particular attention is paid to relative predictive performance under misspecification of the predictive model. Using numerical illustrations, we document several novel findings within this paradigm that highlight the important interplay between the true data generating process, the assumed predictive model and the scoring rule. Notably, we show that only when a predictive model is sufficiently compatible with the true process to allow a particular score criterion to reward what it is designed to reward, will this approach to forecasting reap benefits. Subject to this compatibility however, the superiority of the optimal forecast will be greater, the greater is the degree of misspecification. We explore these issues under a range of different scenarios, and using both artificially simulated and empirical data.

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Section: Introductionsupporting

confidence: 78%

Optimal probabilistic forecasts: When do they work?

Martin¹,

Loaiza-Maya²,

Frazier³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The tail of the distribution is also the main feature of interest when measuring downside risk in equity markets. Besides, Pauwels et al (2020) proposed an approach to computing the optimal weights by maximizing the average logarithmic score subject to additional higher moments restrictions. Through the constrained optimization, the combined probability forecast can preserve specific characteristics of the distribution, such as fat tails or asymmetry.…”

Section: Linear Poolingmentioning

confidence: 99%

Forecast combinations: an over 50-year review

Wang¹,

Hyndman²,

Li³

et al. 2022

Preprint

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Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from the single (target) series is now widely used to improve accuracy through the integration of information gleaned from different sources, thereby mitigating the risk of identifying a single "best" forecast. Combination schemes have evolved from simple combination methods without estimation, to sophisticated methods involving time-varying weights, nonlinear combinations, correlations among components, and cross-learning. They include combining point forecasts, and combining probabilistic forecasts. This paper provides an up-to-date review of the extensive literature on forecast combinations, together with reference to available open-source software implementations. We discuss the potential and limitations of various methods and highlight how these ideas have developed over time. Some important issues concerning the utility of forecast combinations are also surveyed. Finally, we conclude with current research gaps and potential insights for future research.

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“…The frequentist literature includes work on linear combinations (or linear pools), in which various measures of predictive accuracy, including scoring rules, are used to define the criterion that is optimized to estimate the weights. Relevant references here include Hall and Mitchell (2007), Kascha and Ravazzolo (2010), Geweke and Amisano (2011), Ganics (2017), Opschoor et al (2017), Martin et al (2020) and Pauwels et al (2020). Non‐linear weighting schemes (or non‐linear transformations of linear schemes)—either estimated via optimization of prediction‐based criteria, or drawing on the principle of predictive calibration (Dawid, 1982; 1985; Gneiting et al, 2007)— are explored in Ranjan and Gneiting (2010), Clements and Harvey (2011), Gneiting and Ranjan (2013) and Kapetanios et al (2015).…”

Section: Simulation Study: Financial Returnsmentioning

confidence: 99%

Focused Bayesian prediction

Loaiza-Maya

Martin

Frazier

2021

J of Applied Econometrics

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We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After observing data, we update the prior to a posterior over these models, via a criterion that captures a user-specified measure of predictive accuracy. Under regularity, this update yields posterior concentration onto the element of the predictive class that maximizes the expectation of the accuracy measure. In a series of simulation experiments and empirical examples, we find notable gains in predictive accuracy relative to conventional likelihood-based prediction.

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Higher Moment Constraints for Predictive Density Combination

Cited by 5 publications

References 39 publications

Optimal probabilistic forecasts: When do they work?

Optimal probabilistic forecasts: When do they work?

Forecast combinations: an over 50-year review

Focused Bayesian prediction

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