Estimation of the Parameters of a Chirp Type Model with Stationary Residuals

Abstract

Let Xn1,…,Xnn be the observations from a chirp type statistical model Xnt, Xnt=Acos⁡ (ωt+Δ/nt2)+Bsin⁡ ωt+Δ/nt2+ϵt, where ϵt is a stationary noise. We consider a method of estimation of parameters, A, B, ω, Δ, and ν, (where ν is the variance of ϵt’s) which is basically an approximate least-squares method. The main advantage of the proposed approach is that no assumptions are required. We make use of the three theorems which were established associated with the kernel ∑t=1neiut+vt2 and then use them to prove, under certain conditions, the consistency of the estimators.