| Summary: | Signal extraction in tree-ring research is considered as a general time series decomposition problem. A linear aggregate model for a hypothetical ring-width series is proposed, which allows the problem to be reduced to the estimation and extraction of five discrete classes of signals. These classes represent the signals due to trend, climate, endogenous disturbance, exogenous disturbance, and random error. For each class of signal, some mathematical/statistical techniques of estimation are described and reviewed. Except for the exogenous disturbance signal, the techniques only require information contained within the ring-width series, themselves. A unified mathematical framework for solving this decomposition problem has not yet been explicitly formulated. However, the general applicability of ARMA time series models to this problem and the power and flexibility of state space modelling suggest that these techniques will provide the closest thing to a unified framework in the future.
|
|---|
