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時間不均質なオーンシュタイン・ウーレンベック過程の推定

ゲトゥート, プラメスティ GETUT, PRAMESTI 九州大学

2023.03.20

概要

九州大学学術情報リポジトリ
Kyushu University Institutional Repository

Estimation of a time-inhomogeneous Ornstein–
Uhlenbeck process
ゲトゥート, プラメスティ

https://hdl.handle.net/2324/6787424
出版情報:Kyushu University, 2022, 博士(数理学), 課程博士
バージョン:
権利関係:

(様式3)





:Getut Pramesti

論 文 名

:Estimation of a time-inhomogeneous Ornstein–Uhlenbeck process
(時間不均質なオーンシュタイン・ウーレンベック過程の推定)



:甲

















In this thesis, we began by briefly discussing the difficulties in performing
least-squares inference of θ=(λ, A, B, δ) for observations modeled by the time-inhomogeneous
signal processing model in the drift of Ornstein-Uhlenbeck process. We consider a periodic
sinusoidal signal whose is modeled by the kth harmonic of components cos(ωkt)and sin(ω kt)
to have the same periodicity for ωk ≡2πkδ. We use quantization to process a continuous-time
sinusoidal signal into a sequence of numbers, and Euler-Maruyama discretization of the model.
We address the least-squares estimation of the drift coefficient parameter that is
observed at high frequency, in which the discretized step size h satisfies h→0. Under the
conditions nh→∞ and nh²→ 0, we prove the consistency and the asymptotic normality of the
estimators. We obtain the convergence of the parameters at the rate √(nh), except for δ at
√(n3h3).
The numerical examples are presented to verify our theoretical findings and we
illustrate the proposed model by describing the electric power and energy systems, namely
the electricity load from Tokyo Electric Power Company, the energy use of light fixtures in
one Belgium household, France household electric power, and a case study of Tetouan city's
power consumption. The summary of numerical experiments is as follows the proposed model can
be used for medium-term forecasting using hour-by-hour Japan electricity load data; the use
of the periodic model needed a longer time series to estimate the periodicity in the parameter
in the case of energy use in Belgium household; the seasonality of a time-inhomogeneous
Ornstein-Uhlenbeck process led to a good result for very short-term forecasting using
minute-by-minute data; the seasonality of ten minutes of power consumption in the three
networks in Tetouan city can be well approximated by the proposed model, with the same periodic
sinusoidal signal.

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