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AI-GEOSTATS: Fwd: bivariate Ripley's K and time series

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  • Daniel Gavin
    Hello, This is my first posting here, and I apologize if this is off-topic, not being a strictly geostatistics problem. I am considering using the
    Message 1 of 1 , Nov 11, 2003
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      This is my first posting here, and I apologize if this is off-topic,
      not being a strictly geostatistics problem.

      I am considering using the distance-based methods of Ripley's K,
      reduced from two to one dimension and applied to binary time series.
      I have looked for a long time for the appropriate method for my data,
      and I feel this is the most appropriate. So, my question is really
      to see, after reading below, if anyone thinks this is a bad approach.
      In my literature searches, I could not find a similar application of
      the K function, with the possible exception of an article in a
      statistics journal (see below).

      I have two paleoecological records of forest fires, determined from
      charcoal in lake sediment cores, that span the last 5000 years. The
      two records have 23 and 35 fire events, and the error of each fire
      date estimate is about +/- 100 years, based on radiocarbon dates. I
      have two research questions: 1) what is the temporal autocorrelation
      in each record?, and 2) are fires at the two sites occurring
      synchronously, and at what temporal scales are they synchronous?

      For the first question, I used the K function reduced to one
      dimension as suggested for line transect data (Aldrin et al. 2003).
      I used an edge correction, and tested the observed K-hat against
      simulations of randomly ordered intervals between fire events
      (testing whether short intervals are clustered in time). (For
      constructing the 95% confidence envelope, I am not sure if I should
      pick random dates vs. randomly ordering intervals). Done for the
      full 5000 years and for 2000 year subsets, this showed that intervals
      are not clustered. For the second question, I used the bivariate K
      function, where 'attraction' suggests synchrony, and 'repulsion'
      suggests asynchrony. I tested this against simulations of randomly
      shifting the two records relative to each other. This showed no
      dependence (synchrony) between the two sites over the full 5000 years
      at any temporal scale. However, for a few 2000-year subsets, I see
      significant synchrony or asynchrony at scales of about 750 years.

      The only mention I could find for using these methods in the time
      domain is a paper by Doss (1989), which is concerned with proving the
      asymptotic properties of K. The only alternative approach that I
      could find requires grouping fire events into large bins with few
      observations per bin. Any comments or suggestions would be greatly

      Many thanks!
      Dan Gavin

      Aldrin, Holden, and Schweder 2003. Comment on Cowling's "Spatial
      Methods for Line Transect Surveys" Biometrics 59: 186-188.
      Doss, H. 1989. On estimating the dependence between two point
      processes. Annals of Statistics 17:749-763.

      Dan Gavin, Lecturer
      Department of Geography
      94 University Place, 200 Old Mill
      University of Vermont
      Burlington, VT 05405-0114

      Post-Doc Associate
      Department of Plant Biology
      265 Morrill Hall
      University of Illinois
      Urbana, IL 61801

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