Using simulations and data to evaluate mean sensitivity (ζ) as a useful statistic in dendrochronology

Abstract

Mean sensitivity (ζ) continues to be used in dendrochronology despite a literature that shows it to be of questionable value in describing the properties of a time series. We simulate first-order autoregressive models with known parameters and show that ζ is a function of variance and autocorrelation of a time series. We then use 500 random tree-ring data sets with unknown parameters and show that ζ is at best equivalent to the standard deviation of a time series in cases without high autocorrelation and is an inefficient estimator of the coefficient of variation. It is hard to justify the use of ζ as a useful, descriptive statistic in dendrochronology on theoretical or empirical grounds. It is better to make a thorough evaluation of the time series properties of a data set and we suggest various avenues for doing so including some that are maybe unfamiliar to most dendrochronologists including generalized autoregressive conditional heteroscedasticity (GARCH) models.

Citation

Bunn, Andrew G.; Jansma, Esther; Korpela, Mikko; Westfall, Robert D.;Baldwin, James. 2013. Using simulations and data to evaluate mean sensitivity (ζ) as a useful statistic in dendrochronology. Dendrochronologia 31(3): 250-254. doi: https://doi.org/10.1016/j.dendro.2013.01.004.