The use of Inertial Measurement Units (IMU) for navigation purposes is constantly growing and they are increasingly being considered as the core dynamic sensing device for Inertial Navigation Systems (iNS). However, these systems are characterized by sensor errors that can affect the navigation precision of these devices and consequently a proper calibration of the sensors is required. The first step in this direction is usually taken by evaluating the deterministic type of errors, such as bias and scale factor, which can be taken into account through known physical models. The second step consists in finding an appropriate model to describe the stochastic nature of the sensor errors. The focus of this paper is related to the second of such calibration procedures. Indeed, we propose an automatic model selection approach which is particularly appropriate when we observe/collect several independent replicates of the error signal of interest. In short, the proposed approach relies on the Generalized Methods of Wavelet Moments (GMWM) and the Wavelet Variance Information Criterion (WVIC), where we proposed a procedure to compute a Cross-Validation (CV) like estimator of the goodness-of-fit of a candidate model. This estimator provides by construction a tradeoff between model fit and model complexity, therefore allowing rank all candidate models and select the one (or the ones) that appears to be the most appropriate for the task of stochastic sensor calibration.