## 17 Citations

On predictability of ultra short AR(1) sequences

- Computer Science
- 2016

This paper addresses short term forecast of ultra short AR(1) sequences (4 to 6 terms only) with a single structural break at an unknown time and of unknown sign and magnitude with a heuristic result that some universal predictors represented in the frequency domain allow certain predictability based on these ultra short sequences.

On linear weak predictability with single point spectrum degeneracy

- MathematicsApplied and Computational Harmonic Analysis
- 2021

On exact and optimal recovering of missing values for sequences

- Computer Science, MathematicsSignal Process.
- 2017

On exact and optimal recovering of a single missing value

- Mathematics, Computer Science
- 2016

For processes with non-degenerate Z-transform, an optimal recovering algorithm is suggested; this algorithm is based on projections on a closest recoverable sequence; it leads to explicit formulae for the recovered value.

On recovering missing values in a pathwise setting

- Computer Science, MathematicsArXiv
- 2016

In the paper, error-free recoverability is established for classes of sequences with Z-transform vanishing at a point with a rate that can be chosen arbitrarily, and the corresponding recovering kernels are obtained explicitly.

Optimal data recovery and forecasting with dummy long-horizon forecasts

- Computer ScienceArXiv
- 2016

A method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy is suggested, without using probabilistic assumptions on the ensemble.

A Closed Equation in Time Domain for Band-Limited Extensions of One-Sided Sequences

- MathematicsIEEE Transactions on Signal Processing
- 2018

This paper suggests a method of optimal extension of one-sided semi-infinite sequences of a general type by traces of band-limited sequences in deterministic setting, i.e., without probabilistic…

On recovering missing values for sequences in a pathwise setting

- Computer Science
- 2016

The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The…

On sampling theorem with sparse decimated samples: exploring branching spectrum degeneracy

- Mathematics
- 2017

The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and…

## References

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- Mathematics
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Pathwise predictability of continuous-time processes is studied in a deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely,…

Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification

- Mathematics, Computer Science
- 2016

This chapter discusses the development of linear Finite-Dimensional Stochastic Systems with Inputs, and some Topics in Linear Algebra and Hilbert Space Theory.

A general sampling theory for nonideal acquisition devices

- MathematicsIEEE Trans. Signal Process.
- 1994

The authors first describe the general class of approximation spaces generated by translation of a function /spl psi/(x), and provide a full characterization of their basis functions. They then…

Approximating Non-band-limited Functions by Nonuniform Sampling Series

- Computer Science, Mathematics
- 1995

The main purpose of this paper is to show that the approximation error for a series of N terms, which is O (w logw)=N for the usual kernel, is O(w=N for certain other kernels.

Predictors for Discrete Time Processes With Energy Decay on Higher Frequencies

- PhysicsIEEE Transactions on Signal Processing
- 2012

A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies for which the prediction error can be made arbitrarily small.

Predictability on finite horizon for processes with exponential decrease of energy on higher frequencies

- MathematicsSignal Process.
- 2010

Prediction of stable processes: Spectral and moving average representations

- Mathematics, Materials Science
- 1984

SummaryFor stable processes which are Fourier transforms of processes with independent increments, we obtain a Wold decomposition, we characterize their regularity and singularity, and, in the…

Sampling theory in Fourier and signal analysis : advanced topics

- Mathematics
- 1999

1. Applications of sampling theory to combintorial analysis, Stirling numbers, special functions and the Riemann zeta function 2. Sampling theory and the arithmetic Fourier transform 3. Derivative…