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postgraduate thesis: Statistical inference for some discretevalued time series
Title  Statistical inference for some discretevalued time series 

Authors  
Advisors  Advisor(s):Li, WK 
Issue Date  2012 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Wang, C. [王超]. (2012). Statistical inference for some discretevalued time series. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4832951 
Abstract  Some problems of' statistical inference for discretevalued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discretevalued time series data.
The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature.
Besides binary time series, intcgervall1ed time series arc perhaps the most commonly seen discretevalued time series. A generalization of the Poisson autoregression model for nonnegative integervalued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well.
Furthermore, there is an increasing need for models of integervalued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integervalued autoregressive moving average process induced by the socalled signed thinning operator is proposed. The firstorder model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a momentbased estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting onestepahead forecast is also considered based on hidden Markov chain theory.
Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications. 
Degree  Doctor of Philosophy 
Subject  Timeseries analysis. Discretetime systems. Mathematical statistics. 
Dept/Program  Statistics and Actuarial Science 
DC Field  Value  Language 

dc.contributor.advisor  Li, WK   
dc.contributor.author  Wang, Chao   
dc.contributor.author  王超   
dc.date.issued  2012   
dc.identifier.citation  Wang, C. [王超]. (2012). Statistical inference for some discretevalued time series. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4832951   
dc.description.abstract  Some problems of' statistical inference for discretevalued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discretevalued time series data. The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature. Besides binary time series, intcgervall1ed time series arc perhaps the most commonly seen discretevalued time series. A generalization of the Poisson autoregression model for nonnegative integervalued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well. Furthermore, there is an increasing need for models of integervalued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integervalued autoregressive moving average process induced by the socalled signed thinning operator is proposed. The firstorder model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a momentbased estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting onestepahead forecast is also considered based on hidden Markov chain theory. Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.source.uri  http://hub.hku.hk/bib/B48329514   
dc.subject.lcsh  Timeseries analysis.   
dc.subject.lcsh  Discretetime systems.   
dc.subject.lcsh  Mathematical statistics.   
dc.title  Statistical inference for some discretevalued time series   
dc.type  PG_Thesis   
dc.identifier.hkul  b4832951   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Statistics and Actuarial Science   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b4832951   
dc.date.hkucongregation  2012   