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

Mean sensitivity (zeta) 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 zeta 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 zeta 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 zeta 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. (C) 2013 Elsevier GmbH. All rights reserved.