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Moving averages are widely used to estimate time-varying parameters, especially when the underlying dynamic model is unknown or uncertain. However, the selection of the optimal window length over which to evaluate the moving averages remains an unresolved issue in the field. In this paper, we demonstrate the use of Allan variance to identify the characteristic timescales of a noisy random walk from historical measurements. Further, we provide a closed-form, analytical result to show that the Allan variance-informed averaging window length is indeed the optimal averaging window length in the context of moving average estimation of noisy random walks. We complement the analytical proof with numerical results that support the solution, which is also reflected in the authors’ related works. This systematic methodology for selecting the optimal averaging window length using Allan variance is expected to widely benefit practitioners in a diverse array of fields that utilize the moving average estimation technique for noisy random walk signals. 

decrease query response time with limited main memory and storage space, data reduction techniques that preserve data quality are needed. Existing data reduction techniques, however, are often computationally expensive and rely on heuristics for deciding how to split or reduce the original dataset. In this paper, we propose an effective granular data reduction technique for temporal databases, based on Allan Variance (AVAR). AVAR is used to systematically determine the temporal window length over which data remains relevant. The entire dataset to be reduced is then separated into granules with size equal to the AVAR-determined window length. Data reduction is achieved by generating aggregated information for each such granule. The proposed method is tested using a large database that contains temporal information for vehicular data. Then comparison experiments are conducted and the outstanding runtime performance is illustrated by comparing with three clustering-based data reduction methods. The performance results demonstrate that the proposed Allan Variance-based technique can efficiently generate reduced representation of the original data without losing data quality, while significantly reducing computation time.