Time-Series Analyses Applied to Sequences of Nothofagus Growth- Ring Measurements

Time-series analysis, a relatively uncommon technique in ecological studies, has been applied to annual tree growth-ring series. In agreement with earlier North American work, ARMA(1,1) models were found to be the predominant form for expressing stochastic growth processes, occurring in 58% of the 36 Nothofagus menziesii and N. solandri time-series examined. The remaining 42% conformed to an AR(1) process. The average parameter values of {0.79, 0.42} for the ARMA models are remarkably consistent with North American work.
Such derived stochastic models should be regarded as average processes; analyses of first-order autocorrelation coefficients indicate fluctuations in absolute value within series, including some short periods of independence. An apparent preference for a specific ARMA model with species is better explained by the lengths of the series; a shorter time-series is likely to have a simpler stochastic model over time, by virtue of lesser precision associated with model parameters. Thus, 81 % of the series longer than 200 years are modelled by an ARMA(1,1) process, while 78% of the series shorter than 200, are modelled by AR(1).
It is suggested that although fitting Box-Jenkins stochastic models to various genera represents an interesting area of research, the approximate equivalence of the various models, and their part-dependence on series length, negates the need to locate an optimal process in all circumstances. The principal advantage of utilising Box-Jenkins models in this application is to render data more suitable for analysis with environmental variables, and to enhance cross-correlation and mean sensitivity.