The static Allan analysis of variance cannot effectively analyze and identify the random error of a laser gyroscope under static conditions. Further, it cannot provide an accurate basis for the random error compensation of a laser gyroscope under dynamic conditions. Therefore, in this study, we propose a time-frame dynamic Allan analysis of variance method to conduct dynamic Allan analysis of variance and identify the random error terms via piecewise modeling. The grey GM (1, 1) prediction model is established to identify the random error associated with the parameters that have to be predicted. However, the problem of large fluctuation can be observed with respect to the data from the traditional GM (1,1) prediction model is not complete; therefore, we introduce wavelet filters to smoothen the original data and the residual error correction model to improve the GM (1,1) prediction model. The test results denote that the prediction accuracy of the improved GM (1, 1) prediction model is higher than that of the traditional GM (1,1) prediction model for the random error coefficients of laser gyro under the same working condition.