The least-squares estimator of sinusoidal signal of diffusion process for discrete observations

Abstract

There is notably paucity of studies on least-squares estimator of diffusion process for discrete observations. This paper discusses sufficient conditions of the least-squares estimator of diffusion process for discrete observations in order to gain an estimator that is strongly consistent of [1]. We assume that the process Y is arranged by a function such as sinusoidal signal a(θ,Yt) = sin(2πtθ), θ ∈ [0, 1/2] and function b(σ,Yt). For a given a sample (Y₀,Y_h,...,Y_nh), h→0, we demonstrate an asymptotic theory of least-squares estimator θˆn. The results of the study show that the least-squares estimator is strongly consistent and asymptotic normal, assuming that nh→∞ and n³h⁴→∞; θ that represents the frequency of sinusoidal signal of the unity of time which has a rate of convergence, namely √n³h⁴.