Efficient probabilistic forecasts for counts

Brendan McCabe, Gael Martin, David Harris

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Efficient probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution non-parametrically over a given broad model class and proving asymptotic (non-parametric) efficiency in that setting. The method is developed within the context of the integer auto-regressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth-and-death process or branching process. The theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non-parametric estimator relative to a misspecified parametric alternative, in large but finite samples. The method is applied to counts of stock market iceberg orders. A subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given.
Original languageEnglish
Pages (from-to)253 - 272
Number of pages20
JournalJournal of the Royal Statistical Society Series B-Statistical Methodology
Volume73
Issue number2
DOIs
Publication statusPublished - 2011

Cite this

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Efficient probabilistic forecasts for counts. / McCabe, Brendan; Martin, Gael; Harris, David.

In: Journal of the Royal Statistical Society Series B-Statistical Methodology, Vol. 73, No. 2, 2011, p. 253 - 272.

Research output: Contribution to journalArticleResearchpeer-review

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AU - McCabe, Brendan

AU - Martin, Gael

AU - Harris, David

PY - 2011

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AB - Efficient probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution non-parametrically over a given broad model class and proving asymptotic (non-parametric) efficiency in that setting. The method is developed within the context of the integer auto-regressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth-and-death process or branching process. The theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non-parametric estimator relative to a misspecified parametric alternative, in large but finite samples. The method is applied to counts of stock market iceberg orders. A subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given.

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DO - 10.1111/j.1467-9868.2010.00762.x

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