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

• Published in: Dendrochronologia (Verona) Vol. 31; no. 3; pp. 250 - 254
• Main Authors: Bunn, Andrew G., Jansma, Esther, Korpela, Mikko, Westfall, Robert D., Baldwin, James
• Format: Journal Article
• Language: English
• Published: Jena Elsevier GmbH 2013; Elsevier
• Subjects: Autocorrelation; Biological and medical sciences; data collection; dendrochronology; Dendrometry. Forest inventory; Forestry; Fundamental and applied biological sciences. Psychology; growth rings; heteroskedasticity; time series analysis; Time-series model; variance; Autocorrelation; Time-series model; Sensitivity; Simulation; Time series; Data; Models; In series; Dendrochronology; Modeling; Statistics
• ISSN: 1125-7865; 1612-0051
• DOI: 10.1016/j.dendro.2013.01.004

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.