Time-Series Analyses of Tree-Ring Chronologies

Abstract 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.