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Smoothing for discrete-valued time series

Cai, Zongwu, Yao, Qiwei and Zhang, Wenyang (2001) Smoothing for discrete-valued time series. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 63 (2). pp. 357-375. ISSN 1369-7412

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Identification Number: 10.1111/1467-9868.00290


We deal with smoothed estimators for conditional probability functions of discrete-valued time series {Yt} under two different settings. When the conditional distribution of Yt given its lagged values falls in a parametric family and depends on exogenous random variables, a smoothed maximum (partial) likelihood estimator for the unknown parameter is proposed. While there is no prior information on the distribution, various nonparametric estimation methods have been compared and the adjusted Nadaraya–Watson estimator stands out as it shares the advantages of both Nadaraya–Watson and local linear regression estimators. The asymptotic normality of the estimators proposed has been established in the manner of sparse asymptotics, which shows that the smoothed methods proposed outperform their conventional, unsmoothed, parametric counterparts under very mild conditions. Simulation results lend further support to this assertion. Finally, the new method is illustrated via a real data set concerning the relationship between the number of daily hospital admissions and the levels of pollutants in Hong Kong in 1994–1995. An ad hoc model selection procedure based on a local Akaike information criterion is proposed to select the significant pollutant indices.

Item Type: Article
Official URL:
Additional Information: © 2001 The Royal Statistical Society
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 30 Jun 2008 11:03
Last Modified: 20 Feb 2021 03:32
Projects: DMS 0072400, 96/MM109785
Funders: National Science Foundation, University of North Carolina, Biotechnology and Biological Science Research Council Engineering, Physical Science Research Council

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