Inference methods in time-varying linear diffusion processes

In this paper, we introduce a class of inhomogeneous diffusion processes which preserve periodic mean-reverting level and we study the ergodicity of the introduced processes. In particular, the proposed class of processes is suitable for modeling the datasets with a cyclical trend. Such stochastic processes can be used for modeling diverse financial data. We also consider inference problems concerning the drift parameter of the proposed diffusion process. We derive the unrestricted maximum likelihood estimator (UMLE) and the restricted maximum likelihood estimator (RMLE) as well as their joint asymptotic normality. We also construct some shrinkage estimators (SEs) and a test for testing the restriction as well as its asymptotic power. Further, we compare the relative efficiency of the proposed estimators. Finally, the obtained simulation results corroborate our theoretical findings and the applications of the proposed methods are illustrated via an analysis of financial markets.