Stochastic behavior of an instrument is often analyzed by constructing the Allan (or wavelet) variance signatures from an error signal. For inertial sensors, such a signature is conveniently obtained by recording data at rest. The analysis of this signal will result in noise-parameters adequate to such situation. Nonetheless, the value of the noise parameters may change under dynamics or other kind of external influences like for instance the temperature. In this research we study first the influence of the rotational dynamics on the signal of MEMS gyroscopes and then we show how to link this property to the noise-parameter estimation in a rigorous way by a modified version of the Generalized Method of Wavelet Moments (GMWM) estimator. The results of such analysis can then for instance be used in a Kalman filter, where the noise parameters are adapted according to such predetermined functional relationship between sensor noise and the encountered dynamics of the platform/sensor.