Testing Tree-Ring Crossdatings and Other Correlated Time Series by Means of First- and Second-Difference Turn Tests

Abstract

-Two nonparametric tests are presented that are appropriate to, but not limited to, crossdatings of tree-ring chronologies. If each observed measurement in each of two biological time series is rated + or insofar as it is larger or smaller than the preceding observation (commonly the observation of the preceding year), then the presence of correlation between the time series may be detected by forming a 2 X 2 table, entering in its four cells the counts of + +, + -, +, and alignments. This is termed a first-difference turn test. If the turns taken by plots of tree-ring (or other) chronologies are rated R or L insofar as each graph turns to the right or left at each point, as viewed from early to more recent years, then a second-difference turn test can be performed by testing the RR, RL, LR, and LL alignments in a similar 2 X 2 table. These R,L ratings correspond respectively, to +,signs of second-differences. The problem of nonindependence between adjacent +,or R,L ratings is addressed through extensive (300,000+) Monte Carlo chi-square distributions for each test. Modified critical values that compensate for the distortion of the chisquare distribution are presented. A rapid punched-tape procedure for determining 2 X 2 table cell counts is illustrated by a correlation between July-August rainfall and catches of the Atlantic salmon in the Miramichi (New Brunswick, Canada) fishery.