Simulation of the growth ring density of Larix olgensis plantation wood with the ARMA model

Abstract

Because growth ring data have temporal features, time series analysis can be used to simulate and reveal changes in the life of a tree and contribute to plantation management. In this study, the autoregressive (AR) and moving average modeling method was used to simulate the time series for growth ring density in a larch plantation with different initial planting densities. We adopted the Box–Jenkins method for the modeling, which was initially based on an intuitive analysis of sequence graphs followed by the augmented Dickey–Fuller stationarity test. The order p and q of the ARMA (p, q) model was determined based on the autocorrelation and partial correlation coefficient figure truncated on the respective order. Through the residual judgment, the model AR (2) was only fitted to the larch growth ring density series for the plantation with the 1.5 × 2.0 m2 initial planting density. Because the residuals series for the other three series was not shown as a white noise sequence, the modeling was rerun. Larch wood from the initial planting density of 2.0 × 2.0 m2 was modeled by ARMA (2, 1), and ARMA ((1, 5), 3) fitted to the 2.5 × 2.5 m2 initial planting density, and the 3.0 × 3.0 m2 was modeled by AR (1, 2, 5). Although the ARMA modeling can simulate the change in growth ring density, data for the different growth ring time series were described by different models. Thus, time series modeling can be suitable for growth ring data analysis, revealing the time domain and frequency domain of growth ring data.