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Time-Series Analyses of Tree-Ring Chronologies

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The stochastic time-dependent structure of 33 tree-ring series from the dendrochronology literature was analyzed using autoregressive moving average (ARMA) models. Significant autocorrelation was found in every tree-ring series, for not one of the series was white noise. The overall best model was the mixed ARMA(1,1) process. The collection of parameter estimates for this mixed model were tightly clustered, even though the data were collected from the entire length of western North America. High-order autoregressive models (P = 2 to 4) were always a good choice, but usually not as good as the mixed ARMA(1,1) model. Rarely did the first-order autoregressive model provide an adequate description of the data. Standardization (i.e., weighted residuals from the growth trend) of ring-width series into ring-index series was a useful--and often necessary--step for producing a stationary time series. Many of the unstandardized ring-width series demonstrated a strong tendency toward nonstationarity. The practice of removing certain frequencies by passing the data through a running average filter was found to introduce spurious correlations that did not exist in the original data, and thereby obfuscated any statistical analysis in the time domain. The cross correlation function was found to be a useful tool both for examining the association between series and for synchronizing series, especially after prewhitening with appropriate ARMA models. Because significant autocorrelation was found in every series examined, it is recommended that all statistical analyses be performed using the prewhitened residuals from an appropriate ARMA model. Forest Sci. 32:349-372.

Keywords: ARMA models; Box-Jenkins; autoregressive; dendrochronology; moving average

Document Type: Journal Article

Affiliations: Principal Mensurationist, USDA Forest Service, Intermountain Research Station, Forestry Sciences Laboratory, Moscow, ID 83843

Publication date: 1986-06-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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