Smoothing for Discrete-Valued Time Series

Cai, Zongwu and 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. (doi: (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We deal with smoothed estimators for conditional probability functions of discrete-valued time series (Y-1) under two different settings. When the conditional distribution of Y-1 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
Uncontrolled keywords: adjusted Nadaraya-Watson estimator; alpha-mixing; discrete-valued time series; local Akaike information criterion; local linear smoother; local partial likelihood; nonparametric estimation; smoothed maximum likelihood estimation; sparse asymptotics
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Judith Broom
Date Deposited: 20 Nov 2008 19:35 UTC
Last Modified: 29 Apr 2014 15:55 UTC
Resource URI: (The current URI for this page, for reference purposes)
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