The range inter-event process in a symmetric birth-death random walk

Pierre Vallois, Charles Tapiero

Research output: Contribution to journalArticle

Abstract

This paper provides new results for the range inter-events process of a birth-death random walk. Motivations for determining and using the inter-range event distribution have two sources. First, the analytical results we obtain are simpler than the range process and make it easier, therefore, to use statistics based on the inter-range event process. Further, most of the results for the range process are based on long-run statistical properties which limits their practical usefulness while inter-range events are by their nature 'short-term' statistics. Second, in many cases, data on amplitude change are easier to obtain and calculate than range and standard deviation processes. As a results, the predicted statistical properties of the inter-range event process can provide an analytical foundation for the development of statistical tests that may be used practically. Application to outlier detection, volatility and time-series analysis is discussed.

Original languageEnglish (US)
Pages (from-to)293-306
Number of pages14
JournalApplied Stochastic Models in Business and Industry
Volume17
Issue number3
DOIs
StatePublished - Jul 2001

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Random walk
Statistics
Time series analysis
Statistical tests
Range of data
Statistical property
Outlier Detection
Time Series Analysis
Statistical test
Long-run
Volatility
Standard deviation
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Keywords

  • Inter-range events process
  • R/S analysis
  • Range process

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Applied Mathematics
  • Statistics and Probability

Cite this

The range inter-event process in a symmetric birth-death random walk. / Vallois, Pierre; Tapiero, Charles.

In: Applied Stochastic Models in Business and Industry, Vol. 17, No. 3, 07.2001, p. 293-306.

Research output: Contribution to journalArticle

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