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<br />OD3~?S <br /> <br />( <br /> <br />c <br /> <br />6 <br /> <br />improved, unaccountable shifts in critical events occurred due to the effect of mov- <br /> <br />mg averages. <br /> <br />In more recen[ work, lagged tree-ring variables and multi-variate statistical <br /> <br />techniques have been used to determine the sign and magnitude of coefficems used <br /> <br />to transfer ring-width variances and different lags in[o an estimate of specific cli- <br /> <br />matic variables (Stockton, 1971). Box-Jenkins modeling (Box and Jenkins, 1976) <br /> <br />can also be used to determine the appropriate persistence model by successive test- <br /> <br />ing. Models range from a single autoregressive (AR) or moving average (MA) to <br />more complex autoregressive moving average (ARMA). Meko (1981) evaluated <br />both approaches and found that each had advantages and disadvantages depending <br /> <br />on data conditions. Where tree-ring series had considerable autocorrelation, the <br /> <br />Box-Jenkins approach provided a generally flaller response than the lagged predic- <br /> <br />tor method. This evenness of response sacrificed accuracy at longer wave lengths <br /> <br />by underestimating the amplitude of broad swings from the mean. The Box-Jenkins <br /> <br />method is preferable if the ;;pecrrum of the long-term reconsrrucrion i~fJ~st <br /> <br /> <br />because the method anempts to minimize the distortion of persistence. In contrast, <br /> <br />the lagged predictor method ~ccepts frequency distortion as a trade-off forj!igher <br />total variance explained. <br />-- <br /> <br />Landwher and Matalas (1986) used the stochastic properties of tree-ring <br />data to test the desirability of using infinite memory processes in hydrologic simu- <br />lations. Based on examination of 72 dendrochronological records, they found that <br /> <br />fractional gaussian processes (infinite memory) were not the moSt appropriate mod- <br /> <br />els for simulating persistence in the tree-ring data and, by inference, in hydrologic <br /> <br />records. <br />