Some Count Time Series Results
Count time series are now widely encountered in practice. This dissertation contains three projects on count time series. Our first project uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any...
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2023
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ftcdlib:oai:escholarship.org:ark:/13030/qt0sk09442 2023-11-12T04:22:48+01:00 Some Count Time Series Results Kong, Jiajie Lund, Robert 2023-01-01 application/pdf https://escholarship.org/uc/item/0sk09442 en eng eScholarship, University of California qt0sk09442 https://escholarship.org/uc/item/0sk09442 public Statistics etd 2023 ftcdlib 2023-10-23T18:04:30Z Count time series are now widely encountered in practice. This dissertation contains three projects on count time series. Our first project uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The project first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.Our second project reviews and compares popular methods that produce count time series having Poisson marginal distributions. The project begins by reviewing common ways that count series with Poisson marginal distributions can be produced. Statistical estimation methods are next discussed for some of the more worthy methods. Modeling nonstationary series with covariates motivates consideration of methods where the Poisson parameter depends on time. The methods are illustrated in the analysis of two series: 1) a count sequence of major hurricanes occurring in the North Atlantic Basin since 1970, and 2) the number of no-hitter games pitched in major league baseball since 1893.Our third project develops a mathematical model and statistical methods to quantify trends in presence/absence observations of snow cover (not depths) and applies these in an analysis of Northern Hemispheric observations extracted from satellite flyovers during 1967-2021. A two-state Markov chain model with periodic dynamics is introduced to analyze changes in the data in a grid by grid fashion. Trends, converted to the number of weeks of snow ... Thesis North Atlantic University of California: eScholarship |
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University of California: eScholarship |
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English |
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Statistics |
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Statistics Kong, Jiajie Some Count Time Series Results |
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Statistics |
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Count time series are now widely encountered in practice. This dissertation contains three projects on count time series. Our first project uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The project first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.Our second project reviews and compares popular methods that produce count time series having Poisson marginal distributions. The project begins by reviewing common ways that count series with Poisson marginal distributions can be produced. Statistical estimation methods are next discussed for some of the more worthy methods. Modeling nonstationary series with covariates motivates consideration of methods where the Poisson parameter depends on time. The methods are illustrated in the analysis of two series: 1) a count sequence of major hurricanes occurring in the North Atlantic Basin since 1970, and 2) the number of no-hitter games pitched in major league baseball since 1893.Our third project develops a mathematical model and statistical methods to quantify trends in presence/absence observations of snow cover (not depths) and applies these in an analysis of Northern Hemispheric observations extracted from satellite flyovers during 1967-2021. A two-state Markov chain model with periodic dynamics is introduced to analyze changes in the data in a grid by grid fashion. Trends, converted to the number of weeks of snow ... |
author2 |
Lund, Robert |
format |
Thesis |
author |
Kong, Jiajie |
author_facet |
Kong, Jiajie |
author_sort |
Kong, Jiajie |
title |
Some Count Time Series Results |
title_short |
Some Count Time Series Results |
title_full |
Some Count Time Series Results |
title_fullStr |
Some Count Time Series Results |
title_full_unstemmed |
Some Count Time Series Results |
title_sort |
some count time series results |
publisher |
eScholarship, University of California |
publishDate |
2023 |
url |
https://escholarship.org/uc/item/0sk09442 |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_relation |
qt0sk09442 https://escholarship.org/uc/item/0sk09442 |
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public |
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1782337743524724736 |