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Infinitely divisible time series models.

Li, Xuefeng.

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Infinitely divisible time series models.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Infinitely divisible time series models./
作者:	Li, Xuefeng.
面頁冊數:	117 p.
附註:	Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2738.
Contained By:	Dissertation Abstracts International64-06B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3095909

Infinitely divisible time series models.
Li, Xuefeng.

Infinitely divisible time series models. - 117 p.

Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2738.

Thesis (Ph.D.)--University of Pennsylvania, 2003.

In this paper we study time series models with infinitely divisible marginal distributions. The motivation for this study involved a project analyzing call center data. We study several different constructions of a class of autoregressive models and a class of moving average models with Gamma margins. The first one has a form similar to the classical time series ARMA model but with random coefficients. Maximum likelihood, conditional least squares and moment estimates are investigated. Their asymptotic properties are studied. The second construction comes from a general description of Gamma multivariate distributions. The third one generates continuous-time stationary Gamma processes based on the integration of Gamma random fields. All of them yield positively correlated Gamma processes. The last two constructions and most of the corresponding properties carry over to all infinitely divisible distributions with finite second moments. Constructions of higher order autoregressive models are also studied. The covariance structures and connections of those models are investigated. Open questions and future research directions are discussed.Subjects--Topical Terms:

517247
Statistics.

Infinitely divisible time series models.
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245 1 0 $a Infinitely divisible time series models.
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500 $a Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2738.
500 $a Adviser: Lawrence D. Brown.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2003.
520 $a In this paper we study time series models with infinitely divisible marginal distributions. The motivation for this study involved a project analyzing call center data. We study several different constructions of a class of autoregressive models and a class of moving average models with Gamma margins. The first one has a form similar to the classical time series ARMA model but with random coefficients. Maximum likelihood, conditional least squares and moment estimates are investigated. Their asymptotic properties are studied. The second construction comes from a general description of Gamma multivariate distributions. The third one generates continuous-time stationary Gamma processes based on the integration of Gamma random fields. All of them yield positively correlated Gamma processes. The last two constructions and most of the corresponding properties carry over to all infinitely divisible distributions with finite second moments. Constructions of higher order autoregressive models are also studied. The covariance structures and connections of those models are investigated. Open questions and future research directions are discussed.
520 $a Related to these processes we describe a notation of decomposability for infinitely divisible distributions. It is shown that our constructions characterize all infinitely divisible, decomposable stationary processes.
590 $a School code: 0175.
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773 0 $t Dissertation Abstracts International $g 64-06B.
790 1 0 $a Brown, Lawrence D., $e advisor
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