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

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  • Pierre Vallois
  • Charles S. Tapiero

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. Copyright © 2001 John Wiley & Sons, Ltd.

Suggested Citation

  • Pierre Vallois & Charles S. Tapiero, 2001. "The range inter‐event process in a symmetric birth–death random walk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(3), pages 293-306, July.
    • Handle: RePEc:wly:apsmbi:v:17:y:2001:i:3:p:293-306
    DOI: 10.1002/asmb.440
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