Time-temperature superposition (TTS), which for decades has been a powerful method for long-term prediction from accelerated aging data, involves rigid-shifting isotherms in logarithmic time to produce a single master prediction curve. For simple thermo-rheological properties that accurately follow the TTS principle, the shifts can be easily determined, even manually by the eye. However, for many properties of interest, where the principle is obeyed only approximately, or the data is noisy, it is imperative to develop objective shifting techniques along with reliable uncertainty bounds. This work analyzes in detail the method of arclength-minimization as an unsupervised algorithm to determining optimum shifts and demonstrates that the method is nearly unbiased for all practical datasets with a variety of noise distributions. Moreover, if averaged over with-replacement (bootstrap) resamples, the predicted shifts follow a normal distribution, a fact that can be used to construct confidence interval for the master curve through a second-order bootstrap procedure.