Change-point problems in nonlinear regression estimation with dependent observations Original Research Article

Let View the MathML source{Xi,i≥1} and View the MathML source{Yi,i≥1} be stationary sequences of random variables which have some correlation between them. Assume that the relation between {Xi}{Xi} and {Yi}{Yi} can be represented by Yi=m(Xi)+σ(Xi)εi,Yi=m(Xi)+σ(Xi)εi, Turn MathJax on where {εi}{εi} is a sequence of i.i.d. random variables which are independent of {Xi}{Xi} and the nonlinear regression function m(x)m(x) is defined by m(x)=m0(x)+γI[τ,1](x),m(x)=m0(x)+γI[τ,1](x), Turn MathJax on where γ>0γ>0 and m0∈C2m0∈C2. When m(x)m(x) is smooth except for at t=τt=τ, ττ is called a change-point of the regression function m(x)m(x). We consider estimation of the change-point ττ in the case when the sequence of random variables View the MathML source{(Xi,Yi),i≥1} satisfies the strong mixing condition from the viewpoint of time series analysis for mathematical finance.