Optimal data recovery and forecasting with dummy long-horizon forecasts
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The paper suggests a method of recovering of missing values based on optimal approximation by band-limited processes for sequences, i.e. discrete time processes, that are not necessarily band-limited. The problem is considered in the pathwise setting, without using probabilistic assumptions on the ensemble. The method requires to solve a closed linear equation in the time domain connecting the available observations of the underlying process with the values of the band-limited process outside the observation range. Some robustness with respect to noise contamination is established for the suggested recovering algorithm. It is suggested to apply the data recovery algorithm to a forecasting problem considered as a data recovery problem that is solvable via interpolation with a dummy long-horizon forecast.
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