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This study analyzed the relationship between characteristics of annual tree ring time series and the intensity of attacks on forest stands by forest insects. Using tenets of the fluctuation–dissipation theorem (which is widely used in physics), time series parameters are proposed that can help to assess the susceptibility of a forest stand to insect pests. The proposed approach was applied to evaluate differences in parameters of tree ring widths among outbreaks of the pine looper, Siberian silk moth, and spongy moth. A comparison of trees characteristics between outbreak locations and undamaged forest stands (control) showed that the tested parameters statistically significantly differed between the outbreak locations and control stands and can be used to assess the risk of pest outbreaks in forest stands.