Asymptotic behavior of maximum likelihood estimator for time inhomogeneous diffusion processes
Abstract
We study asymptotic behavior of maximum likelihood estimator for a time inhomogeneous diffusion process given by a SDE dXt=α b(t)Xt dt + σ(t) dBt, t∈[0,T), with a parameter α∈ R, where T∈(0,∞] and (Bt)t∈[0,T) is a standard Wiener process. We formulate sufficient conditions under which the MLE of α normalized by Fisher information converges to the limit distribution of Dickey-Fuller statistics. Next we study a SDE dYt=α b(t)a(Yt) dt + σ(t) dBt, t∈[0,T), with a perturbed drift satisfying a(x)=x+O(1+|x|γ) with some γ∈[0,1). We give again sufficient conditions under which the MLE of α normalized by Fisher information converges to the limit distribution of Dickey-Fuller statistics.
0