Estimating trends in tree-ring data

Two methods from econometrics are introduced to estimate growth trends in time series of ring widths or basal-area increments. First, a trend model is described with a stochastic level and slope. The second model combines a doubly differenced trend and an ARMA model additively. Both models are put into a state-space form and are estimated using the discrete Kalman filter. Unknown noise variances, which control the flexibility of the trends, can be estimated by maximum-likelihood optimization or chosen by hand. It is concluded that the trend plus AR (1) model in combination with ML estimation performs very well. This model is attractive, because the ML-estimation procedure enables an objective choice for unknown parameters. Examples are given of two special features: the prediction of future growth, and the weighing of missing or unreliable data. Finally, both models are compared with spline interpolation and are validated by means of simulated time series.