Signal Processing Of The One-Factor Mean-Reverting Model In Energy System - Pramesti, Getut; Saptono, Ristu (Journal of the Indonesian Mathematical Society, 2025)
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, $nh→ ∞$, and $nh^{2}→ 0$. This paper shows that the frequency component estimator in the one-factor mean-reverting 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 $\frac{1}{6}(1+θ^{2})$. We applied the proposed model to the energy systems data.