On the estimation of periodic signals in the diffusion process using a high-frequency scheme
-
Getut Pramesti
and
Ristu Saptono
Abstract
The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude.
The periodicity of the frequency components is also thought to affect the convergence of these parameters.
In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal.
Under the high-frequency sampling setting, we provide the frequency components’ consistency and asymptotic normality.
It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl.
29 (2023), 1, 1–32].
The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic.
In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components.
Further, the result of the study, that is, the convergence rate of the frequency is
Acknowledgements
The author is grateful to Professor Karl Sabelfeld for his remarks.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Option pricing: Examples and open problems
- A wavelet-based method in aggregated functional data analysis
- Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary
- On the estimation of periodic signals in the diffusion process using a high-frequency scheme
- Strong approximation of a two-factor stochastic volatility model under local Lipschitz condition
- Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations
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Articles in the same Issue
- Frontmatter
- Option pricing: Examples and open problems
- A wavelet-based method in aggregated functional data analysis
- Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary
- On the estimation of periodic signals in the diffusion process using a high-frequency scheme
- Strong approximation of a two-factor stochastic volatility model under local Lipschitz condition
- Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations
- Asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system
