On some quasi-periodic approximations

Poghosyan, Arnak; Poghosyan, Lusine; Barkhudaryan, Rafayel

doi:10.52737/18291163-2020.12.10-1-27

Cited by 3 publications

(2 citation statements)

References 24 publications

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“…Это более корректный вариант, однако он усложняет модель, зависит от ее свойств и спецификации и не является универсальным. Применительно к задаче оценки кривой доходностей смотрите, например, работы [6][7][8].…”

Section: обзор литературыunclassified

Treatment of Missing Market Data: Case of bond Yield Curve Estimation

Makushkin,

Lapshin

2023

jour

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Missing observations in market data is a frequent problem in financial studies. The problem of missing data is often overlooked in practice. Missing data is mostly treated using ad hoc methods or just ignored. Our goal is to develop practical recommendations for treatment of missing observations in financial data. We illustrate the issue with an example of yield curve estimation on Russian bond market. We compare three methods of missing data imputation — last observation carried forward, Kalman filtering and EM–algorithm — with a simple strategy of ignoring missing observations. We conclude that the impact of data imputation on the quality of yield curve estimation depends on model sensitivity to the market data. For non-sensitive models, such as Nelson-Siegel yield curve model, final effect is insignificant. For more sensitive models, such as bootstrapping, missing data imputation allows to increase the quality of yield curve estimation. However, the result does not depend on the chosen data imputation method. Both simple last observation carried forward method and more advanced EM–algorithm lead to similar final results. Therefore, when estimating yield curves on the illiquid markets with missing market data, we recommend to use either simple non-sensitive to the data parametric models of yield curve or to impute missing data before using more advanced and sensitive yield curve models.

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Section: обзор литературыunclassified

Treatment of Missing Market Data: Case of bond Yield Curve Estimation

Makushkin,

Lapshin

2023

jour

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“…Over the last two decades, several Armenian researchers have made significant contributions to the Lanczos approach. For instance, the works of A. Nersessian and A. Poghosyan addressed the main issue of some alternatives to the quasi-Bernoulli series in [67,[87][88][89][90][91][92], such as the quasi-polynomial series, the Fourier-Pade series, the trigonometric interpolations series, and the quasi-polynomial Pade series. Similarly, A. Nersessian studied a framework based on a biorthogonal system and adaptive algorithms with a strong potential for accelerating the convergence of Fourier series due to an over-convergence phenomenon [93][94][95][96].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Potential of Mixed Fourier Series in Signal Processing Applications Using One-Dimensional Smooth Closed-Form Functions with Compact Support: A Comprehensive Tutorial

Páez-Rueda,

Fajardo,

Pérez

et al. 2023

MCA

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This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its application in signal processing, especially because it allows us to control the decreasing rate of Fourier coefficients and avoids the Gibbs phenomenon. Therefore, this method improves the signal processing performance in a wide range of scenarios, such as function approximation, interpolation, increased convergence with quasi-spectral accuracy using the time domain or the frequency domain, numerical integration, and solutions of inverse problems such as ordinary differential equations. Moreover, the paper provides comprehensive examples of one-dimensional problems to showcase the advantages of this approach.

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On the Convergence of the Quasi-Periodic Approximations on a Finite Interval

Poghosyan

Barkhudaryan

2021

Armen. J. Math.

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We investigate the convergence of the quasi-periodic approximations in different frameworks and reveal exact asymptotic estimates of the corresponding errors. The estimates facilitate a fair comparison of the quasi-periodic approximations to other classical well-known approaches. We consider a special realization of the approximations by the inverse of the Vandermonde matrix, which makes it possible to prove the existence of the corresponding implementations, derive explicit formulas and explore convergence properties. We also show the application of polynomial corrections for the convergence acceleration of the quasi-periodic approximations. Numerical experiments reveal the auto-correction phenomenon related to the polynomial corrections so that utilization of approximate derivatives surprisingly results in better convergence compared to the expansions with the exact ones.

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On some quasi-periodic approximations

Cited by 3 publications

References 24 publications

Treatment of Missing Market Data: Case of bond Yield Curve Estimation

Treatment of Missing Market Data: Case of bond Yield Curve Estimation

Exploring the Potential of Mixed Fourier Series in Signal Processing Applications Using One-Dimensional Smooth Closed-Form Functions with Compact Support: A Comprehensive Tutorial

On the Convergence of the Quasi-Periodic Approximations on a Finite Interval

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