Autoregressive moving average models of crown profiles for two California hardwood species

Time-series Autoregressive Moving Average (ARMA) models were employed to model tree crown profiles for two California hardwood species (blue oak and interior live oak). There are three major components of these models: a polynomial trend, an ARMA model, and unaccounted for variation. The polynomial trend was used to achieve a stationary series. For these crown profiles, the use of a quadratic trend resulted in a stationary series for 60% of the profiles. A cubic trend was used for another 23%, and a quartic for 7%. It was found that 80% of the tree crown profiles could be modeled using a first order ARMA model [AR(1), or MA(1)] in conjunction with a polynomial trend and another 10% as a polynomial trend with white noise. 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. Using a binary classification scheme it was possible to relate the type of ARMA model needed for a crown profile series to tree size and stand characteristics.