AI-GEOSTATS: Fwd: bivariate Ripley's K and time series
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
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
Department of Plant Biology
265 Morrill Hall
University of Illinois
Urbana, IL 61801
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