Smoothing for discrete-valued time series

Zongwu Cai (), Qiwei Yao and Wenyang Zhang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: adjusted Nadaraya–Watson estimator; discrete-valued time series; local akaike information criterion; local linear smoother; local partial likelihood; nonparametric estimation; smoothed maximum likelihood estimation; sparse asymptotics. (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

Published in Journal of the Royal Statistical Society. Series B: Statistical Methodology, 2001, 63(2), pp. 357-375. ISSN: 1369-7412

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Journal Article: Smoothing for discrete‐valued time series (2001)
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