Autoregressive Moving Average Models of Conifer Crown Profiles

A time-series autoregressive moving average (ARMA) approach was used to develop stochastic models of tree crown profiles for five conifer species of the Sierran mixed conifer habitat type. Models consisted of three components: (1) a polynomial trend; (2) an ARMA model; and (3) random error. A Bayesian information criterion was used to evaluate alternative models. It was found that 70% of the crown profiles could be modeled using first-order ARMA [AR(l) or MA(l)] models, and that an additional 25% could be modeled using a white noise model [(AR(O)]. When the coefficients of the ARMA models were statistically significant, the models proved to be both visually and statistically an improvement over the polynomial trend (a Euclidean model). A binary classification system was used to determine if model type was related to tree or stand characteristics. Using this classification we found that it was possible to relate the appropriate model type to forest tree size and forest stand density with acceptable accuracy.