In this article, we introduce a generalized Cox-Ingersoll-Ross (GCIR) model tailored to capture periodic financial data patterns, including those influenced by structural changes. This model is particularly suited for applications where data exhibit non-stationarity and lack explicit trajectories, addressing challenges often encountered in real-world financial and economic analyses. We study the drift parameter estimation problem for the GCIR process under potential parameter restrictions. In particular, we derive both the Unrestricted and Restricted Maximum Likelihood Estimators along with their joint asymptotic normality. These theoretical advancements enable us to construct shrinkage estimators. A key practical contribution of this work is a novel method for estimating the location of a change-point in GCIR, essential for identifying structural shifts in financial time series. We further analyze the asymptotic distributional risk of the proposed estimators and evaluate their relative efficiency. Our theoretical findings are supported by extensive simulations and a case study analyzing historical corn price data, demonstrating the model’s utility in real-world settings. By addressing critical challenges in non-stationary data modeling, this work contributes significantly to the practical application of stochastic processes in financial and economic studies.