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Abstract

A system and method model a time series from missing data by imputing missing values, denoising measured but noisy values, and forecasting future values of a single time series. A time series of potentially noisy, partially-measured values of a physical process is represented as a non-overlapping matrix. For several classes of common model functions, it can be proved that the resulting matrix has a low rank or approximately low rank, allowing a matrix estimation technique, for example singular value thresholding, to be efficiently applied. Applying such a technique produces a mean matrix that estimates latent values, of the physical process at times or intervals corresponding to measurements, with less error than previously known methods. These latent values have been denoised (if noisy) and imputed (if missing). Linear regression of the estimated latent values permits forecasting with an error that decreases as more measurements are made.

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