Pathwise continuous time spectrum degeneracy at a single point and weak predictability
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The paper studies properties of continuous time processes in pathwise deterministic setting with spectrum degeneracy at a single point where their Fourier transforms vanish. It appears that these processes are predictable in some weak sense, meaning that convolution integrals over future time can be approximated by causal convolutions over past time with kernels; these predicting kernels are selected independently on the inputs. The paper obtains corresponding predictors explicitly. The predictors feature some robustness with respect to noise contamination.
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