Description: The purpose of this paper is to help practitioners and regulators more accurately quantify the potential impact of market risk on insurance products with equity-linked guarantees. To this end, this paper examines time series model selection and assessment based on residuals, with a focus on regime switching models. Also it discusses the difficulties in defining residuals for such processes and propose several possible alternatives. We determine that a stochastic approach to defining the residuals is the only way to generate residuals that are normally distributed under the model hypothesis.