On detecting predictability of one-sided sequences

We consider predicting and predictability for discrete time processes in a pathwise setting where only a sole one-sided semi-infinite sequence of past values is available, and where statistical properties of the ensemble of the paths are unknown. We obtain some sufficient conditions of predictability in the terms of degeneracy of frequency characteristics representing one-sided modifications of the Z-transform. These characteristics are defined for one-sided semi-infinite sequences representing of the past values. Some predictors are discussed

On causal extrapolation of sequences with applications to forecasting

The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for forecasting. This lead to a forecasting method for more general sequences without this feature based on minimization of the mean square error between the observed path and a predicable sequence. These procedure involves calculation of this predictable path; the procedure can be interpreted as causal smoothing. The corresponding smoothed sequences allow unique extrapolations to future times that can be interpreted as optimal forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670