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Time-series Imputation Algorithm



David A. Howe, Chloe Champagne


Statistical imputation is a field of study that attempts to fill missing data. It is commonly applied to population statistics whose data have no correlation with running time. For a time series, data is typically analyzed using the autocorrelation, the Fourier transform to estimate power spectral density (PSD), trends, the Allan deviation (ADEV), and basically any analysis that depends on uniform time indexes. We describe an imputation algorithm that fills multiple gaps in a time series. We create an example in which four massive gaps exceed 100% of the original time series. We show that the PSD with imputation applied to the gaps is essentially the same as the original. Also, the confidence of ADEV with imputation falls within 90% of the original ADEV. The algorithm in Python is included for those wishing to try it.
IEEE Signal Processing Letters


ADEV, convolution, dead-time, frequency, gaps, imputation, missing data, power-law noise models, Python, sparce, time, time-series.


Howe, D. and Champagne, C. (2021), Time-series Imputation Algorithm, IEEE Signal Processing Letters, [online],, (Accessed April 17, 2024)
Created November 5, 2021, Updated March 26, 2024