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The Sun-Baked Speculator
Tom Ryan

The Dendrochronology Posts

Dendrochrology #1 (05/16/2003):
Met a very interesting gent who works in the tree ring lab at the university. It would seem that this is very much a statistical science with possibly some overlap to our world. We measure prices and use them to indirectly make observations about bias and probabilities. The tree folks measure rings and use them as an indirect measure of climate and precip probabilities. Also both have a-periodic disturbances (wildfires, bear markets) within their records. Both have some autoregressive character. Both measure individual elements (stocks-trees) and composite to wholes (indices). Both have some fundamental organizing principles including supply-demand. these can be very long term records. Look at the one he forwarded to me from some trees near to where our cabin is. The record stretches back to the 1590s. Also gave me this interesting url (http://web.utk.edu/~grissino/) which has a link to the int'l tree ring database. Has anyone been down this road before. I am headed down it for awhile.

Dendrochronology #2 (5/19/03):
At first glance the natural philosopher would tend to think that evaluating tree growth to back calculate or study cycles or to study natural law would be adding another messy layer of independent variables that would make analysis more difficult and make it harder to draw meaningful analogies. Better to just work with direct natural events such as rainfall records or earthquake records or flood records or temperature records.

Yes--but the aforementioned events are all environmental, non-animus, while the tree is a living, growing thing capable of adapting and evolving which makes it actually more applicable than one would think at first glance. The tree rings show us the result of not only these climate and environmental inputs but how the tree responds and reacts to them - as well as the effects wrought on the tree by its neighbors, survival of fittest, etc. Overall a good place for the statistically inquisitive I think.

Dendrochronology #3 (5/20/3)
some preliminary thoughts. The obvious ones

• there are phases to the growth rate, accelerating rate early on, then a high but declining rate followed by a mature phase at a relatively flat rate of growth, and then decline to death.
• although there is survivor bias involved here in the data set, life is resilient. even in bad years there is some growth. even in the arid southwest US.
• growth volatility, year to year, as measured by variance of last 10 year data set (or 20 or 30) is much higher in early years then when older.
• there are multi-year cycles with some autocorrelation, but these cycles are aperiodic:
  • for example with tree AZ726011 a big cone douglas fir near baldy peak arizona the cycles of growth occurred:
  • highs: 1629, 1661, 1680, 1751, 1810, 1917, 1949
  • lows: 1648, 1673, 1724, 1782, 1880, 1926
• there is some mean reverting nature to the growth in the sense of each tree having a certain capability for growth over a long period (100 years).
• there are fat tails to the tree ring widths whereby there are more extremely good/bad years than would be expected from a gaussian distribution.

Dendrochronology #4 (5/27/3)
continuing on, i find some interesting statistics for a grove of old douglas fir near baldy peak arizona.

• the deviations for any given year from an average of previous 5-10 years are much higher on the negative side than on the positive side: there tends to be a non-symmetric disn around the moving average and a higher tendency to experience a sudden crash in terms of growth than to suddenly have a extremely flourishing year.
• survivor graphs (periodicity of extremely bad years) are power laws. if one was to look at the mature growth phase of tree AZ726011 (last 162 years), and using mean-1.3 std deviations to define drought years (19 years of 162 fit criterion), this would yield the probability of experiencing a bad year as
  • 66% within 5 years
  • 78% within 10 years
  • 90% within 15 years
  • 95% within 20 years
  longest period without difficult conditions (as defined above) 37 years. this compares to a survivor function for the dow for a 25% decline condition of
  • 55% within 5 years
  • 76% within 10 years
  • 83% within 15 years
  • 92% within 20 years
  • 99% within 25 years
  yes storks and babies, but similar shapes and magnitudes is my point.
• there is a tendency, far above random, for bad years to cluster back to back. e.g. for the definition above there are 19 difficult years: 1847, 1851, 1857, 1860/1861 , 1873/1874/1875, 1879/1880/1881, 1894, 1904, 1922/1923/1924/1925, 1962/1963, 1973. notice clustering. if random walk then the prob of back to back difficult years is .01 (0.1^2). yet of 18 pairs, 9 occur back to back.
• for the last 162 years of data, the correlation coefficient of growth one year and growth the next is 0.32. correlation coefficient values in the .1-.4 range seem typical of the data that i have seen for that particular type of tree for that particular area of arizona. these coefficients are positive, meaningful, but not extraordinarily high.

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