Concordance: A Measure of Similarity Between Matrices of Time Series with Applications in Dendroclimatology

A fundamental assumption in dendroclimatology is that the common signal produced by multiple trees of the same species, growing under similar environmental conditions within the same climate region, relates to changes in the climate within that region in the same way. However, there are concerns that the climate response of young kauri trees may differ to older kauri. As a result, the inclusion of radii from young kauri may weaken the climate signal of the composite chronology. To address this concern, a subset of the data containing tree rings formed when the trees were young was compared to those formed when the trees were old. These subsets contained time series of correlated tree rings aligned by year with start and end years differing for each series. Existing techniques for comparing subsets of time series lack reliability for ragged arrays of dependent non-stationary time series. The concordance method was developed to overcome this. Concordance is a non-parametric method based on bootstrapping that is used to test the hypothesis that two subsets of time series are similar in terms of mean, variance or both. Simulations show that concordance is effective for detecting difference in both the level and scale of two submatrices containing non-stationary and dependent time series. When applied to tree-ring data, the concordance method was able to detect evidence against the subset of young tree rings having the same mean, variance or both than older, more established trees.