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Title: On cumulative process model and its statistical analysis (English)
Author: Volf, Petr
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 36
Issue: 2
Year: 2000
Pages: [165]-176
Summary lang: English
Category: math
Summary: The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the cumulative rate of the process. We prove the uniform consistency of the estimator and the asymptotic normality of the process of residuals. On this basis, the goodness- of-fit test and the test of homogeneity are proposed. We also give an example of application to analysis of financial transactions. (English)
Keyword: counting processes
Keyword: martingales
Keyword: estimators
MSC: 60G55
MSC: 62G05
MSC: 62M07
MSC: 62M09
MSC: 62P05
idZBL: Zbl 1248.62138
idMR: MR1760023
Date available: 2009-09-24T19:31:55Z
Last updated: 2015-03-26
Stable URL:
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