SIGNAL PROCESSING OF THE ONE-FACTOR MEAN-REVERTING MODEL IN ENERGY SYSTEM Getut Pramesti and Ristu Saptono
Universitas Sebelas Maret
Abstract
One of the models that can be considered in the energy system is the one-factor mean-reverting process. We propose the one-factor mean-reverting model with sinusoidal signal processing involved. The frequency component of the model can be estimated with a high-frequency scheme. The estimation of the frequency component is believed to produce a precise estimate. This is because the high-frequency scheme has the potential to handle possible non-linear coefficient cases in a unified way, that is, -nh\to \infty-, and -nh^{2}\to 0-- which is mentioned in \cite{pramesti2022parameter}.
This paper shows that the frequency component estimator in the one-factor mean-reverting strong model is strongly consistent with the rate convergence, namely -\sqrt{(nh)^3}-. It is also can be shown that the estimator has a normal approximation with a mean of 0 and variance -\frac{1}{6}(1+\theta^{2})-. We applied the proposed model to the energy systems data.
