Testing the stability of transfer functions

In dendroclimatology, testing the stability of transfer functions using cross-calibration verification (CCV) statistics is a common procedure. However, the frequently used statistics reduction of error (RE) and coefficient of efficiency (CE) merely assess the skill of reconstruction for the validation period, which does not necessarily reflect possibly instable regression parameters. Furthermore, the frequently used rigorous threshold of zero which sharply distinguishes between valid and invalid transfer functions is prone to an underestimation of instability. To overcome these drawbacks, we here introduce a new approach – the Bootstrapped Transfer Function Stability test (BTFS). BTFS relies on bootstrapped estimates of the change of model parameters (intercept, slope, and r²) between calibration and verification period as well as the bootstrapped significance of corresponding models. A comparison of BTFS, CCV and a bootstrapped CCV approach (BCCV) applied to 42,000 pseudo-proxy datasets with known properties revealed that BTFS responded more sensitively to instability compared to CCV and BCCV. BTFS performance was significantly affected by sample size (length of calibration period) and noise (explained variance between predictor and predictand). Nevertheless, BTFS performed superior with respect to the detection of instable transfer functions in comparison to CCV.