Efficient probabilistic forecasts for counts

• 成果类型: Article
• 署名作者: McCabe, Brendan P. M.; Martin, Gael M.; Harris, David
• 署名单位: Monash University; University of Liverpool; University of Melbourne
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2010.00762.x
• 发表日期: 2011
• 页码: 253-272
• 关键词: time-series; models

摘要

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.