Estimating Trends and Stochastic Response Functions in Dendroecology with an Application to Fir Decline

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Abstract
A regression model is introduced to estimate a trend and, possibly time-dependent, regression coefficients simultaneously. The model is meant to detect time-dependencies in the response of tree growth to environmental conditions. The existing models in this field usually ignore these time evolutions. The trend is modeled via a doubly differencing scheme, while the regression coefficients, i.e., the response function, may vary in a nearly arbitrary, stochastic way. The estimation is performed via the discrete Kalman filter. Unknown noise variances, which control the flexibility in time of the stochastic parameters, are estimated using maximum likelihood optimization. The model is applied to four ring-width chronologies of European silver firs (Abies alba Mill.) in the Bavarian Forest, Germany. Monthly averaged temperatures and monthly sums of precipitation are used as explanatory variables, together with an index series of SO2 emissions in the former Federal Republic of Germany. The latter variable is argued to be a reliable pollution indicator. It appears that the dramatic growth variations of silver firs since 1960 cannot solely be explained by meteorological variables. Furthermore, a strong relationship is found between the high frequency parts of both the ring-width signal and the SO2 emission series since 1945. For. Sci. 38(2):221-234.

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